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Quadratics Lesson 2: Graphing Quadratic Equations
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[Solved] Unit 8: Quadratic Equations Date: Bell: Homework 2
The graph of a quadratic equation is a parabola or a 2nd degree curve. To plot the equation, these are the steps: Substitute values of x to determine their …
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Date Published: 8/4/2022
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Unit 8: Graphing Quadratic Functions – algebrataylor
Unit 8: Graphing Quadratic Functions ; 3/17, 8.2 – Graphing Equations in Standard Form, 8.2 Day 2 Worksheet ; 3/20, 8.2 – Quadratic Equation Story Problems, 8.2 …
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Date Published: 2/11/2022
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Unit 8: Quadratic Functions
8.1 – Transformations, Characteristics, & Graphs of Quadratic Functions. Days 1/2 – January 22nd … 8.2 – Equations & Applications of Quadratic Functions.
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Date Published: 6/5/2021
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Copy Of Unit 8: Quadratic Equations – Lessons – Blendspace
Copy of Unit 8: Quadratic Equations. by Holly Irby. Day 1: Kuta Worksheet (Sle 5). Day 2: p257 in workbook and the Khan Academy Quiz (Sle 10).
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Date Published: 8/19/2022
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STUDENT TEXT AND HOMEWORK HELPER – Sharyland ISD
Write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x – h)2 + k), …
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Quadratic Equations UNIT BUNDLE! – PDF Free Download
11 Name: Date: Bell: Unit 8: Quadratic Equations Homework 2: Graphing Quadratic Equations Graph each quadratic equation by making a table.
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Unit 8: Quadratic Equations – Homework 1 – Instructure
2. The curve formed by a quadratic equation is called a parabola … If the vertex is the highest point on the graph, it is called a __Maximum.
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Unit 8: Introduction to Quadratic Functions and Their Graphs
You can find the y by plugging x into your equation. Example 2: Find the vertex and the axis of symmetry for the following functions. a) y = 2×2 + 4x b …
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Unit 8: Graphing Quadratic Functions
Below the table are notes and videos. Date What did we learn today? Homework 3/14 8.1 – Introduction to quadratic functions
8.1 Worksheet
3/15 8.1 – Introduction to quadratic functions
8.1 Day 2 Worksheet
3/16
8.2 – Introduction to the standard form
8.2 Worksheet
3/17 8.2 – Representation of equations in standard form
8.2 Day 2 Worksheet
3/20
8.2 – Story problems with quadratic equations
8.2 Worksheet for Day 3
3/21 8.1-8.2 Quiz review
8.1-8.2 Quiz Review
3/22 8.1-8.2 quizzes
none
27.3
8.3 – Graphing equations in vertex form
8.3 Worksheet
28.3
8.4 – Graphing equations in factored form
8.4 Worksheet
29.3
8.3-8.4 Quiz Review
8.3-8.4 Quiz Review
30.3
8.3-8.4 Quizzes
none
31.3
Unit 8 review
test Tuesday
4/3
Unit 8 review
Unit 8 review
4/4
Unit 8 test
none
VIDEOS:
Squares in standard form (8.2):
Quadratic functions in standard form – ORR
Finding the vertex from the standard form – ORR
CLASS NOTES & ANSWER KEY:
Copy of Unit 8: Quadratic Equations
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Quadratic Equations UNIT BUNDLE!
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1 Quadratic Equations UNIT BUNDLE!
2 Quadratic Equations: Example Unit Outline DAY 1 TOPIC Introduction to Quadratic Equations: Symmetrical Axis, Vertex, Minimum, Maximum, Parabolas HOMEWORK HW #1 DAY 2 Graphing Quadratic Equations HW #2 DAY 3 Square Roots HW #3 DAY 4 Quiz 8- 1 None DAY 5 Solving Squares by Factoring (Day 1) HW #4 DAY 6 Solving Squares by Factoring (Day 2) HW #5 DAY 7 Review of Solving Squares by Factoring Study DAY 8 Quiz 8-2 None DAY 9 The Quadratic Formula HW # 6 DAY 10 Factoring vs. Quadratic Formula: Choosing the Best Method. HW #7 DAY 11 Solving Squares Using the Square Root Method (ax 2 + c = 0) HW #8 DAY 12 Review: Solving Squares Using All Methods HW #9 DAY 13 DAY 14 DAY 15 DAY 16 Quiz 8-3 Area Tasks; Start Projectile Motion Projectile Motion Linear vs. Quadratic Models None HW #10 HW #11 TAG 17 Quadratic Inequalities HW #12 TAG 18 Unit Review; Complete Study Guide Study DAY 19 TEST None See sample page images on next page.
3 Name: Class: Subject: Date: Main ideas/questions Standard form Diagram Types of parabolas Notes All quadratic equations are written in the form: When graphed, a quadratic equation produces a U-shaped curve called a. Use your graphing calculator to plot: y = x 2 + 2x 5 y = -x 2 + 3x + 7 When a is then the parabola opens up like a smile. If a is then the parabola opens like a frown axis Symmetry formula for the symmetry axis: Vertex When the vertex is the lowest point, it is called a. When the vertex is the highest point, it is referred to as a. Examples 1. y = x 2 + 8x + 15 Axis of symmetry: Vertices: Sketch: Gina Wilson, 2013
4 2. y = -x x 23 axis of symmetry: vertex: sketch: 3. y = 3x 2 12x + 5 axis of symmetry: vertex: sketch: 4. y = 4x 2 + 8x 1 axis of symmetry: vertex: sketch: 5. y = -x 2 4x 2 axis of symmetry: vertex: sketch: 6. y = 2x 2 12x + 9 axis of symmetry: vertex: sketch: 7. y = -3x 2 24x 42 axis of symmetry: vertex: sketch: 8. y = -x 2 + 4x axis of symmetry: Vertex: Sketch: 9. y = x 2 3 Axis of symmetry: Vertex: Sketch: 10. y = -2x Axis of symmetry: Vertex: Sketch: Gina Wilson, 2013
5 Name: Date: Bell: Unit 8: Quadratic equations Homework 1: Introduction to quadratic Complete the following statements. ** This is a 2 page document! ** 1. The standard form of a quadratic equation is. 2. The curve formed by a quadratic equation is called a. 3. The formula for the axis of symmetry is 4. If the vertex is the highest point of the graph, it is called a. 5. If a node is the lowest point on a graph, it is called a. Find the axis of symmetry and the vertex for the following quadratic equations. Then sketch the parabola and label all parts. 6. y = x 2 + 6x + 4 axis of symmetry: vertex: sketch: 7. y = -2x 2 + 8x 5 axis of symmetry: vertex: sketch: 8. y = x 2 2x axis of symmetry: vertex: sketch: 9. y = – x 2 8x 9 Axis of Symmetry: Vertex: Sketch: Gina Wilson, 2013
6 10. y = -5x 2 20x 26 axis of symmetry: vertex: sketch: 11. y = x 2 4 axis of symmetry: vertex: sketch: 12. y = -x 2 + 2x 4 axis of symmetry: vertex: sketch: 13. y = – 3x 2 Axis of symmetry: Vertex: Sketch: 14. y = 2x 2 12x + 10 Axis of symmetry: Vertex: Sketch: 15. y = x 2 +10x + 24 Axis of symmetry: Vertex: Sketch: Gina Wilson, 2013
7 SHOWING QUADRATIC EQUATIONS y = ax 2 + bx + c Steps to draw a quadratic equation: Step 1: Find the axis of symmetry. Step 2: Find the vertex. Step 3: Fill in a table of values with your calculator. Step 4: Chart! Work out! Draw each quadratic equation. 1. y = x 2 axis of symmetry: x y vertex: domain of definition: area: 2. y = x 2 + 2x + 5 axis of symmetry: x y vertex: domain of definition: area: 3. y = -x 2 8x 17 axis of symmetry: x y vertex: domain: Area: Gina Wilson, 2013
8 4. y = -2x 2 + 4x + 1 Axis of symmetry: x y Vertex: domain: range: 5. y = x 2 6x + 13 Axis of symmetry: x y Vertex: domain of definition: range: 6. y = -x 2 4 Axis of symmetry: x y Vertex: area: area: 7. y = 2x 2 + 8x Axis of symmetry: vertex: x y area: area: Gina Wilson, 2013
9 8. y = -x 2 + 4x + 3 Axis of symmetry: x y Vertex: Domain: Region: 9. y = -x 2 2x Axis of symmetry: Vertex: x y Domain: Region: 10. y = -3x 2 18x 20 Axis of symmetry: Vertex :xy domain:area:Gina Wilson, 2013
10 Analyzing Quadratic Graphs GRAPH A GRAPH B Answer the questions about the graphs above. 1. What is the symmetry axis of graph A? 2. What is the symmetry axis for graph B? 3. What is the vertex of graph A? maximum or minimum? 4. What is the vertex of graph B? maximum or minimum? 5. Identify the domain and range of graph A. 6. Identify the domain and range of graph B. 7. Identify the equation for graph A: A y = x 2 4x 1 C y = -x 2 4x 1 B y = x 2 + 4x 1 D y = -x 2 + 4x 1 8 Identify the equation for graph B: A y = x 2 6x 5 C y = -x 2 6x 5 B .y = x 2 + 6x 5 D y = -x 2 + 6x 5 Gina Wilson, 2013
11 Name: Date: Bell: Unit 8: Quadratic equations Homework 2: Graphing quadratic equations Graph each quadratic equation by creating a table. 1. y = x x + 26 ** This is a 2 page document! ** Axis of symmetry: Vertex: Domain: x y area: 2. y = -2x 2 + 8x Axis of symmetry: Vertex: Domain: x y area: 3. y = x 2 2x Axis of symmetry: Vertex: Domain: x y area: 4. y = – x 2 8x 16 axis of symmetry: vertex: domain: x y domain: Gina Wilson, 2013
12 5. y = 3x 2 5 axis of symmetry: vertex: domain: x y range: 6. y = -2x x 15 axis of symmetry: vertex: domain: x y range: 7. y = -x axis of symmetry: vertex: range: x y range: 8 .y = 2x 2 16x + 30 Axis of symmetry: Vertex: Area: x y area: Gina Wilson, 2013
13 Name: Class: Topic: Date: Main ideas/questions Notes Definition Also called number of 2 SOLUTIONS 1 SOLUTION NO SOLUTION Sample solutions 1. y = x 2 + 4x 5 x y Find the solutions of the following squares by graphing. Solutions: y = x 2 2x + 1 x y y = -x 2 + 2x 3 x y Gina Wilson, 2013
14 solutions: 4. y = x 2 10x + 16 x y y = -x x y 6. y = -3x 2 + 6x x y The discriminant formula: If d > 0, then there are solutions. If d = 0 then there are solutions. If d < 0, then there are solutions. Examples Use the discriminant to find the number of solutions. 7. y = x 2 + 5x y = x 2 3x y = x x y = 2x 2 4x y = 4x 2 12x y = -3x 2 + 5x 8 Gina Wilson, 2013 15 Name: Unit 8: Quadratic Equations Date: Bell: Homework 3: Quadratic Roots ** This is a 2 page document! ** 1. The points where a quadratic equation intersects the x-axis are denoted as: Graph the quadratic equation and find the solution(s). 2. y = x 2 + 2x 3 3. y = x 2 8x + 12 x y x y solutions: solutions: 4. y = x y = -x x 21 x y x y solutions: solutions: 6. y = x 2 4x y = -2x 2 8x x y x y solutions: Solutions: Gina Wilson, 2013 16 8. y = x 2 6x y = x 2 + 4x + 9 x y x y Solutions: Solutions: Use the discriminant to determine the number of solutions. 10. y = x 2 3x y = 2x 2 4x y = -3x 2 + 5x y = x 2 5x y = -x 2 + 2x y = 4x 2 9 Gina Wilson, 2013 17 Ticket name: Graph the quadratic equation by filling in a table of values. Then fill in the blanks. 1) y = -x 2 6x 5 x y axis of symmetry: vertex: range of values: range: zeros: FLIP! Ticket name: Graph the quadratic equations by filling in a table of values. Then fill in the blanks. 1) y = -x 2 6x 5 x y axis of symmetry: vertex: range of values: range: zeros: FLIP! 18 2) y = x 2 + 4x + 4 x y-axis of symmetry: vertex: domain: range: zeros: 2) y = x 2 + 4x + 4 x y-axis of symmetry: vertex: domain: range: zeros: 19 Name: Date: Bell: Algebra I Honors Unit 8: Quadratic Equations Quiz 8-1: Graphing Quadratic Equations. 1. The standard form of a quadratic equation. 2. The U-shaped curve generated by a quadratic equation. 3. The vertical line dividing the parabola into two equal parts. 4. The formula for the axis of symmetry. 5. The turning point of a parabola. 6. A vertex, which is the highest point. A d = b 2 4ac B Minimum C Axis of symmetry D y = ax 2 + bx + c E Parabola F Vertex 7 A vertex that is the lowest point. G x = b 2a 8. The points where the parabola intersects the x-axis. 9. Used to determine the number of solutions to a quadratic equation. 10. The formula for the discriminant. H Maximum I Zeros J Discriminant Find the symmetry axis and vertex for the following quadratic equations: 11. y = -x 2 2x 8 symmetry axis: vertex: 12. y = 2x symmetry axis: vertex: Fill in the spaces in the following diagrams. 13. Axis of symmetry: Vertex: Domain: Range: Roots: Equation: A y = x 2 + 6x 5 C y = -x 2 + 6x 5 B y = x 2 6x 5 D y = -x 2 6x5 Gina Wilson, 2013 20 14. Axis of symmetry: Vertex: Definition range: Value range: Roots: Equation: A y = x 2 + 2x + 1 C y = x 2 2x + 1 B y = -x 2 + 2x + 1 D y = - x 2 2x Axis of symmetry: Vertex: Domain: Region: Roots: Equation: A y = x 2 + 8x 17 C y = x 2 8x 17 B y = -x 2 + 8x 17 D y = -x 2 8x Axis of symmetry: Vertex: Domain: Region: Zeros: Equation: A y = x 2 4x C y = x 2 + 4x B y = x 2 4 D y = x Use the discriminant to find the number of solutions. 17. y = x 2 10x y = -3x 2 + 7x y = -x y = 2x 2 + 9x 2 1 Gina Wilson, 2013 21 Quadratic Equations in Vertex Form What is vertex form? y = a(x h) 2 + k where (h, k) is the vertex of the parabola. How do we convert this back to standard form standard form? Use! 1. =( 2) +3 axis of symmetry: x y vertex: domain: domain: 2. =2( +3) 1 axis of symmetry: x y vertex: domain: domain: 3. = ( 2) +1 axis of symmetry: x y vertex: domain: Area: Gina Wilson, 2013 22 Solving Squares by Factoring Objective: Find quadratic solutions (roots, roots, etc.) by factoring rather than graphing. Example: Find the solutions of the equation = + by factoring. Step 1: Set the quadratic equation equal to 0. Step 2: Factor the left side. Step 3: Set each factor e equal to 0 and solve for x. Step 4: Write your answer in curly brackets. It's your turn! Solve the squares by factoring. 1st x 2 + 4x + 3 = 0 2nd x x + 24 = 0 3rd x 2 + x 2 = 0 4th x 2 + 6x 27 = 0 5th x 2 10x + 21 = 0 6th x 2 x 20 = 0 7. x x + 25 = 0 8. x 2 8x + 16 = 0 9. x 2 8x = x x = 0 Gina Wilson, 2013 23 11. 6x 2 12x = x 2 6x = x 2 64 = x 2 25 = x 2 81 = x 2 49 = 0 equations NOT in standard form orm you must MOVE-FACTOR-SOLVE! 17. x2 + 4x = x2 45 = 4x 19. x2 5x 64 = 7x 20. x2 10x + 49 = 4x x2 = 28x x2 = x2 + 8x 23. x2 = x2 = 9 gina Wilson, 2013 24 Name: Unit 8: Quadratic Equations Date: Bell: ** This is a 2 page document! ** Solve any quadratic equation by factoring. 1. x 2 + 7x + 12 = 0 2. x 2 8x 9 = 0 Homework 4: Solving squares by factoring (Day 1) 3. x 2 x 30 = 0 4. x 2 8x = x 2 10 = 9x 6 .x x = x x 2 3x + 16 = 7x 8. x 2 + 3x 5 = x 2 x 46 = 3x x 2 14x 18 = -8x 2 Gina Wilson, 2013 25 11. 2x 2 7x + 4 = x x 2 + 3x = x x = x 2 3x = x 2 = 36x 16. x 2 36 = x 2 49 = x 2 = 1 Gina Wilson, 2013 26 SOLVING SQUADRATICS BY FACTORING Day 2 Slip & Slide IMPORTANT: If you can factor a by GCF, DO NOT use Slip & Slide! Example 1: Example 2: 3x 2 + 9x 12 = 0 5x 2 20x 60 = 0 Example 3: Example 4: 2x 2 + 3x 5 = 0 8x 2 22x + 5 = 0 Try it now! 1. 2x x + 8 = x 2 24x 28 = x x 10 = x 2 8x + 3 = 0 Gina Wilson, 2013 27 5. 3x x + 15 = x x 7 = x 2 21x + 4 = x 2 + 5x + 1 = x 2 8x 5 = x x + 9 = x 2 + 7x = x = 10x x x = x 2 + 7x = x Gina Wilson, 2013 28 Name: Unit 8: Quadratic Equations Date: Bell: ** This is a 2 page document! ** Solve any quadratic equation by factoring. 1. 2x 2 8x 24 = x 2 + 5x 30 = 0 Homework 5: Solving squares by factoring (Day 2) 3. 4x x + 8 = x 2 15x + 12 = x 2 7x 6 = x 2 + 5x + 3 = x 2 19 x 5 = x 2 x 2 = 0 Gina Wilson, 2013 29 9. 6x 2 + 7x + 2 = x 2 11x + 2 = x 2 14x = x = 11x x = 5x x + 11 = -6x x 2 = 17x = 12x 4x 2 Gina Wilson, 2013 30 Name: Date: Bell: Algebra I Honors Unit 8: Quadratic Equations Solve the following quadratic equations by factoring. Quiz 8-2: Solving Squares by Factoring = =0 Answers = = = = = = = =24 B = =25 Bonus: Solve the quadratic equation + = Gina Wilson, 2013 31 Write quadratic equations by identifying the roots! 1y = ( )( ) 2y = ( )( ) 3y = ( )( ) 4y = ( )( ) Gina Wilson, 2013 32 The quadratic formula = ± Some problems cannot be solved by factoring. The quadratic formula can be used in this situation to find the square roots. Example: Solve x 2 6x + 4 = 0 using the quadratic formula. More practice! 1st x x 2 = 0 2nd x 2 11 = 4x 3rd x 2 8x = x 2 5x 36 = 0 5th x 2 + 6x + 10 = x 2 12x 18 = 0 Gina Wilson, 2013 33 7. -x 2 + 7x 3 = 0 8. x 2 + 4x + 1 = x = 7 x x x = x 2 + 5x + 4 = x 2 + 7x 9 = x 2 8 = x = 12x 15. 3x 2 1 = -8x 16. 3x 2 + 7x = x 2 2x + 15 Gina Wilson, 2013 34 Name: Date: Bell: Unit 8: Quadratic Equations Homework 6: Solving Quadratic Equations Using the Quadratic Formula ** This is a 2 page document! ** Solve any quadratic equation by quadratic formula. 1. x 2 + 4x 3 = x = 9x = ± 3. x 2 = -5x x 2 3x + 1 = 6 5. x 2 + 4x + 17 = 8 2x 6. 4x 2 6x 1 = 0 Gina Wilson, 2013 35 7. 5x 2 3x 1 = x 2 + 7x 18 = x 2 25 = x 2 7x 4 = x 2 4x 11. 8x 2 5 = -4x 12. 4x 2 18x = 0 Gina Wilson, 2013 36 Factoring vs. Quadratic Formula It is much more efficient to use factoring when possible, although the quadratic formula will work in all cases. Choose the most appropriate method to solve the following quadratic equations: =0 2 4 = = = = =0 7 42= = = =21 Gina Wilson, 2013 37 = = = = = = = = = =3 12 Gina Wilson, 2013 38 Name: Date: Bell: Unit 8: Quadratic Equations Homework 7: Solving Quadratic Equations Review Factoring / Quadratic Formulas ** This is a 2 page document! ** Use factorization or the quadratic formula to solve the following. 1. x 2 8x 20 = x 2 15x = x 2 25 = 0 4. x 2 8x 2 = 0 5. x 2 + 3x 40 = 0 6. x 2 15 = 0 7. x = 14x 8. 3x 2 + x 1 = 0 Gina Wilson, 2013 39 9. 18x 2 = 24x 10. x 2 7x + 12 = 3x x 2 11x + 28 = x 2 1 = 3x 2 + 9x 13. x 2 5 = x 2 5x = x 2 = x 2 1 = 5 3 Gina Wilson, 2013 40 Solving Quadratic Equations: Square Root Method Today we are going to solve quadratic equations using square roots. This method only works if there is no x term. + = Steps Step 1: Isolate x 2 = Step 2: Extract the SQUARE ROOT from both sides Directions: Use the square root method to solve any quadratic equation: 1. 16= = = = =4 6. 5= = = = = ==16 Gina Wilson, 2013 41 = = = = = =8 19. = = = = = = = =7 27. ( 17)= = = =46 What time is it? Gina Wilson, 2013 42 Name: Unit 8: Quadratic Equations Date: Bell: Homework 8: Solving Quadratic Equations by Square Roots ** This is a 2 page document! ** Solve any quadratic equation using the square root method. 1. x 2 49 = x 2 18 = x 2 20 = 0 4. x = 0 5. x 2 24 = x 2 22 = x = 8. 1 x 2 1 = x 2 25 = x 2 = 49 Gina Wilson, 2013 43 11. 81x 2 = x 2 7 = x = x 2 3 = x 2 6 = x 2 = x 2 92 = x 2 15 = x = x = x = 22. x = Gina Wilson, 2013 44 Group members: Bell: REVIEW: Solving quadratic equations Work through each problem with your group members. Each person in the group should participate and write on their own paper. Factorization: = = = =0 Square roots: 5. = = = =16 The quadratic formula: = =0 Gina Wilson, 2013 45 = =3 YOUR CHOICE! ========4+7 Gina Wilson, 2013 46 Name: Date: Bell: Unit 8: Quadratic Equations Homework 9: Solving Quadratic Equations Review (all methods) ** This is a 2 page document! ** Use factoring, the square root method, or the quadratic formula to solve the following. 1. x 2 8x 20 = x 2 15x = x 2 25 = 0 4. x 2 8x 2 = 0 5. x 2 + 3x 40 = 0 6. x 2 15 = 0 7. x = 14x 8. 3x 2 + x 1 = 0 Gina Wilson, 2013 47 9. 18x 2 = 24x 10. x 2 7x + 12 = 3x x 2 11x + 28 = x 2 1 = 3x 2 + 9x 13. x 2 5 = x 2 5x = x 2 = x 2 1 = 5 3 Gina Wilson, 2013 48 Name: Date: Bell: Algebra I Honors Unit 8: Quadratic Equations Quiz 8-3: Solving Quadratic Equations (All Methods) SOLVE BY FACTORING, SQUARE ROOTS, or QUADRATIC FORMULA 1. x 2 6x + 5 = 0 2. x 2 10x = 4 = ± answers x 2 = x 2 3x 18 = x x 2 = 9x x 2 + 3x = x 2 14x = 0 x 2 8 = x x = 5x x 2 11 = 84 Gina Wilson, 2013 49 area problems with quadratic equations! 1 Using the chart below, find the value of x when the area of the rectangle is 78 square meters. 2 Using the chart below, find the dimensions of the rectangle when the area of the rectangle is 108 square meters. x x 3 x + 7 x 3 Use the chart below to find the dimensions of the rectangle when the area is 128 square feet. 4 The dimensions of a rectangle can be expressed as x + 3 and x 8. If the area of the rectangle is 60 square inches, what is the value of x? x 1 x The length of a rectangular garden is 4 meters more 6 than its width. The area of the rectangle is 60 meters. Find the dimensions of the rectangle. The length of a rectangle is 6 meters less than its width. Find the dimensions of the rectangle when its area is 27 square meters. Gina Wilson, 2013 50 BULLET MOVEMENT 1. A soccer ball is kicked off the ground with an initial upward velocity of 90 feet per second. The equation = + gives the height of the ball after seconds. a. Find the maximum height of the ball. 1a. b. b. How many seconds does it take for the ball to hit the ground? 2. An apple is thrown straight up from an 80 foot platform at 64 feet per second. The equation for the height of this apple at time seconds after launch is = a. b. a. Find the maximum height of the apple. b. How many seconds does it take for the apple to reach the ground? 3. In science class, students were asked to make a container for an egg. They then dropped this container out of a window 25 feet off the ground. The equation = + gives the height of the container in seconds. 3a. b. a. Find the maximum height of the container. b. How many seconds does it take for the container to reach the ground? Gina Wilson, 2013 51 4. A penny is dropped from the Empire State Building, which is 1,250 feet tall. If the path of the penny can be modeled by the equation = + how long would it take for the penny to hit a 6 foot person? Some fireworks are fired vertically into the air from the ground at an initial velocity of 80 feet per second. The equation for the altitude of this object at time seconds after launch is = +. How long does it take for the fireworks to hit the ground? The Apollo s Chariot, a roller coaster at Busch Gardens, moves at 110 feet per second. The equation of the ride can be represented by the equation = + +. What is the maximum altitude reached by this ride? Eva jumps on a trampoline. Their height at time can be modeled by the equation = + +. Would Eve reach a height of 14 feet? An astronaut on the moon throws a baseball up at an initial speed of 10 meters per second and releases the baseball 2 meters off the ground. The baseball path equation can be modeled by = The same experiment is performed on Earth by modeling the path by the equation = How long would the ball stay in the air longer on the moon compared to Earth? 8.Gina Wilson, 2013 52 Name: Unit 8: Quadratic Equations Date: Bell: Homework 10: Quadratic Word Problems ** This is a 2 page document! ** Area problems: 1. Using the following diagram, determine the value of x when the area is 21 square meters. x 2. The dimensions of a rectangle can be given by x + 7 and x + 2. If the area of the rectangle is 66 square inches, what are the dimensions of the rectangle? x 4 3. The length of a rectangle is 6 meters greater than its width. If the area of \u200b\u200bthe rectangle is 135 square meters, find its dimensions. 4. The length of a rectangle is 1 meter less than its width. The area of the rectangle is 42 square meters. Find the dimensions of the rectangle. Projectile Motion Problems: 5. When a cannonball is fired, the trajectory equation can be modeled by h = -16t t. a. Find the maximum height of the cannonball. b. Find out how long it takes for the cannonball to hit the ground. Gina Wilson, 2013 53 6. When Joey jumps off a diving board, the equation of his path can be modeled by h = -16t t a . Find Joey's maximum size. b. Find out the time it takes Joey to reach the water. 7. A toy rocket is launched from a 48 foot high platform. The height of the rocket above the ground is modeled by h = -16t t a . Find the maximum height of the rocket. b. Calculate the time it takes for the rocket to reach the ground. 8. At the end of the school year, Rachel and Amber go to the top of a 12 story building and throw their algebra book over the edge. The equation for the path each girl's textbook takes is given below. By how many seconds does Rachel's textbook knock Ambers down? Rachel: h=-16t t Amber: h=-16t t Gina Wilson, 2013 54 Linear vs. Quadratic Models LINEAR QUADRATIC Equation: Equation: Directions: Use a graph to determine the model. Then find the equation for the best fit. 1 2 x y x y linear or quadratic? Equation: 3 x y linear or quadratic? Equation: x y linear or quadratic? Equation: linear or quadratic? Equation: Gina Wilson, 2013 55 5 6 x y x y linear or quadratic? Equation: x y linear or quadratic? Equation: x y linear or quadratic? Linear or square? 9 Equation: The value V of a computer between 1999 and 2003 is given in the table. Equation: t V Linear or Quadratic? Equation: value of the computer in 2008? 10 A coin is tossed from the top of the Statue of Liberty, which is 305 feet above the ground. The height h of the coin is recorded after each second t in the table below. t h linear or quadratic? Equation: Height of coin after 7s? Gina Wilson, 2013 56 Name: Date: Bell: Unit 8: Quadratic Equations Homework 11: Linear and Quadratic Models ** This is a 2 page document! ** Determine if a linear or quadratic model exists. Then find the equation for the best fit x y x y linear or quadratic? Equation: x y linear or quadratic? Equation: x y linear or quadratic? Equation: linear or quadratic? Equation: 5. A real estate agent tries to determine the relationship between a 3 bedroom house's distance from New York City and its median selling price. It records the data for 6 houses shown below. x y 755, , , , , ,000 *x = miles from NYC; y = housing costs linear or quadratic? Approximate cost of a home 90 miles from NYC? Equation: Gina Wilson, 2013 57 6. A soccer ball is kicked into the air with an initial upward velocity of 82 feet per second. Its altitude, h (in feet), is recorded at various seconds, t, in the following table. t h linear or quadratic? Equation: height of football after 5 seconds? 7. A frog jumps on a lily pad. Its altitude, h (in feet), is recorded at various seconds, t, in the following table. t h linear or quadratic? Equation: jet height after 6 sec? 8. The table below shows the number of students enrolled at Mapleton High School since x y. Linear or square? Equation: Number of students to enroll in 2011? Gina Wilson, 2013 58 Ticket Name: Determine whether the following data represents a linear or quadratic model. Then solve for the missing value using the equation for the best-fit line or curve. 1) The local theater puts on a play every year. The following table shows the number of auditions for the lead role each year since approximating the number of auditions that will occur in Year Auditions using an equation to model the data. ) A toy rocket was launched into the air. The height h of the rocket at time t seconds is recorded in the table below. Using an equation to model the data, find the rocket's altitude after 5 seconds. t (sec) h (ft) Ticket Name: Determine whether the following data represents a linear or quadratic model. Then solve for the missing value using the equation for the best-fit line or curve. 1) The local theater puts on a play every year. The following table shows the number of auditions for the lead role each year since approximating the number of auditions that will occur in Year Auditions using an equation to model the data. ) A toy rocket was launched into the air. The height h of the rocket at time t seconds is recorded in the table below. Using an equation to model the data, find the rocket's altitude after 5 seconds. t (sec) h (feet) 59 SQUARE INEQUALITIES Step 1: Find the and. Step 2: Use your calculator to create a table of values. Step 3: Draw the parabola. *Use a line for < or > symbols. *Use line for or symbols. Step 4: Use a to determine where to shade. EXAMPLES: 1. > x y x y 3. < x y x y Gina Wilson, 2013 60 5. < x y x y < x y x y < x y x y Gina Wilson, 2013 61 Name: Date: Bell: Unit 8: Quadratic Equations Homework 12: Quadratic Inequalities ** This is a 2 page document! ** Instructions: Graph the following quadratic inequalities. Shade the possible solutions. 1. y > x 2 + 2x 3 2. y 2x 2 12x y < -x 2 + 8x y < x 2 4x y -2x x y 3x x + 25 Gina Wilson, 2013 62 7. y x 2 6x 8. y > -x 2 + 4x 7 9. y 2x 2 4x 10. y < -x Gina Wilson, 2013 63 Topic #1: Axis of Symmetry and Vertex 1. = Unit 8 Test Study Guide Quadratic Equations 2. = = 9 Axis of Symmetry Vertex Axis of Symmetry Vertex Axis of Symmetry Vertex Topic #2: Graphing of Quadratic Equations 4. y = x 2 8x + 15 Axis of Symmetry: Vertices: area: range: zeros: 5. y = -x 2 + 4x 4 Axis of symmetry: vertices: area: area: zeros: 6. y = -2x 2 3 Axis of symmetry: vertices: area: range of values: zeros: topic #3 : Solving quadratic equations (by factoring!) 7. 7 = = +2 Gina Wilson, 2013 64 = = = = = = = =24 Topic #4: Solving quadratic equations (using the quadratic formula!) 17. = = = =81 Gina Wilson, 2013 65 Topic #5: Area Issues 21. If the area of the rectangle below is 42 square inches, find the value of x. x The length of a rectangle is five feet less than its width. If the area of the rectangle is 84 square feet, find its dimensions. x + 8 Topic #6: Projectile Motion 23. Natalie found a tennis ball outside of a tennis court. She picked up the ball and threw it over the fence onto the pitch. The ball's path can be represented by h = -16t t + 5 a. Find the maximum height of the tennis ball. b. How long does it take to reach the ground? 24. A circus acrobat is shot out of a cannon with an initial upward velocity of 50 ft/s. The equation for the acrobat's path can be modeled by h = -16t t + 4. a. Find the maximum height of the acrobat. b. How long does it take to reach the ground? Topic #7: Linear and quadratic modeling 25. Debbie recorded the time it took seven children of different ages to complete one lap around the track. Use an equation to model the data and find the approximate time it would take a 6-year-old to run one lap. AGE (years) TIME (secs) A pistol is accidentally shot vertically in the air. The height h of the bullet at time t seconds is recorded in the table below. Use an equation to model the data and find the gun's elevation after 10 seconds. t (sec) h (ft) Gina Wilson, 2013 66 UNIT 8 TEST REVIEW Find someone who! Instructions: Exchange papers with 12 different people to solve the following problems. Find the axis of symmetry and the vertex for the following quadratic equation: 1 2 Identify the factors of the following quadratic equation. Write your answers in the boxes. y = -x 2 + 8x 23 axis of symmetry vertex name: name: 3 Write the following quadratic equation in standard form. y = (x 3) Lösen durch Faktorisieren: x 2 30 = 7x 5 Name: Lösen durch Faktorisieren: 6 Name: Lösen durch Faktorisieren: 3x 2 + 3x = 60 10x x = 2x + 6 s Name: Name: Gina Wilson, 2013 67 7 Lösen durch Faktorisieren: 8 Lösen durch Faktorisieren: 12x 2 20x = 0 2x 2 = x Name: Lösen durch Faktorisieren: (x + 9)(x 2) = Name: Welche quadratische Gleichung hat Wurzeln von -5 und 2? A. y = x 2 + 3x 10 B. y = x 2 3x 10 C. y = x 2 + 7x + 10 D. y = x 2 7x + 10 Name: Name: Die Höhe eines in die Luft geschossenen Pfeils kann durch die Gleichung h = -16t t + 6 dargestellt werden, wobei t die Zeit in Sekunden und h die Höhe in Fuß ist. 11 Wie hoch darf der Pfeil maximal sein? 12 Wie lange braucht der Pfeil, um den Boden zu erreichen? Name: Name: Gina Wilson, 2013 68 Name: Datum: Bell: Algebra I Test Einheit 8 (quadratische Gleichungen) ZEIGEN SIE ALLE AUFGABEN, DIE ERFORDERLICH SIND, UM JEDE FRAGE ZU BEANTWORTEN! PLATZIEREN SIE IHRE LETZTE ANTWORT IN DAS FELD. VIEL GLÜCK! 1. Finden Sie die Symmetrieachse und den Scheitelpunkt für die folgende Gleichung. y = -x 2 4x Finden Sie die Symmetrieachse und den Scheitelpunkt für die Gleichung unten. y = 2x Symmetrieachse Scheitelpunkt Symmetrieachse Scheitelpunkt 3. Verwenden Sie das Diagramm unten, um die Lücken zu füllen. Symmetrieachse: Scheitelpunkt: Domäne: Bereich: Nullstellen: Gleichung: A. y = x 2 + 2x + 3 C. y = -x 2 + 2x + 3 B. y = x 2 2x + 3 D. y = -x 2 2x Welcher Graph stellt die Gleichung y = (x + 2)(x 4) dar? A. B. C. D. Gina Wilson, 2013 69 5. Wählen Sie zwei Binome aus, die die Faktoren der in der Grafik gezeigten Parabel darstellen könnten. Schreiben Sie Ihre Antworten in die Kästchen. x + 2 x 2 x + 7 x 7 y = ( )( ) 6. Wählen Sie die Gleichung(en) aus, die die unten abgebildete Parabel darstellen könnten. y = (x 5)(x + 1) y = x 2 4x 5 y = (x + 5)(x 1) y = (x + 2) 2 9 y = x 2 + 4x 5 y = (x 2) Welche Gleichung ist äquivalent zur folgenden Gleichung? y = (x 2) Finden Sie die Lösung(en) der folgenden Gleichung. x x = 24 A. y = x 2 1 B. y = x C. y = x 2 4x 1 D. y = x 2 4x Finde die Lösung(en) der folgenden Gleichung. x x = 4x Finden Sie die Lösung(en) der folgenden Gleichung. 4x 2 24 = 20x Gina Wilson, 2013 70 11. Finden Sie die Lösung(en) der folgenden Gleichung. 5x x = x Finden Sie die Lösung(en) der folgenden Gleichung. x 2 9x = Finden Sie die Lösung(en) der folgenden Gleichung. 4x = Finden Sie die Lösung(en) der folgenden Gleichung. (x 1)(x + 3) = Finden Sie die Lösung(en) der folgenden Gleichung. (x 4) 2 = Die Gewinngleichung für ein produzierendes Unternehmen lautet P = x , wobei P der Gewinn und x die Anzahl der verkauften Einheiten ist. Ab welcher Stückzahl verkauft das Unternehmen die Gewinnschwelle? (P = 0) A. 50 verkaufte Einheiten B. 100 verkaufte Einheiten C. 500 verkaufte Einheiten D verkaufte Einheiten 17. Welche Gleichung hat die Wurzeln -2 und 3? 18. A. y = x 2 + x 6 B. y = x 2 x 6 C. y = x 2 + 5x + 6 D. y = x 2 5x + 6 Finden Sie die Lösung(en) für die folgende Gleichung. x 2 + 7 x 10 = 0 Gina Wilson, 2013 71 19. Finden Sie die Lösung(en) der nachstehenden Gleichung. 3x 2 = x Wenn die Fläche des Rechtecks unten 39 Quadratfuß beträgt, ermittle den Wert von x. x 2 x Wählen Sie die quadratische(n) Gleichung(en) mit zwei Wurzeln aus. y = x 2 8x 20 y = x y = x 2 2x + 1 y = x 2 25 y = 4x x April schießt einen Pfeil mit einer Geschwindigkeit von 80 Fuß pro Sekunde von einer 25 Fuß hohen Plattform nach oben. Der Pfad des Pfeils kann durch die Gleichung h = -16t t + 25 dargestellt werden, wobei h die Höhe und t die Zeit in Sekunden ist. Was ist die maximale Höhe des Pfeils? A. 80 Fuß B. 90 Fuß C. 125 Fuß D. 140 Fuß 23. Ein Stein fällt von einer Brücke 320 Fuß über einem Fluss. Der Weg, den der Stein nimmt, kann durch die Gleichung h = -16t modelliert werden. Wie lange braucht der Stein, um den Fluss zu erreichen? A. 2,5 Sek. B. 3,5 Sek. C. 3,8 Sek. D. 4,5 Sek. Gina Wilson, 2013 72 24. Die Tabelle zeigt die Einschreibung von Studenten an einer Hochschule nach Jahr. Ermitteln Sie mithilfe einer Gleichung zur Modellierung der Daten die ungefähre Einschreibung für das Jahr x y A Personen B Personen C Personen D Personen 25. Der Sears Tower ist mit 1.451 Fuß eines der höchsten Bauwerke in den Vereinigten Staaten. Ein Penny wird von der Spitze des Turms geworfen. Die Höhe h des Pennys wird nach jeder Sekunde t in der Tabelle aufgezeichnet. Verwenden Sie eine Gleichung, um die Daten zu modellieren, und finden Sie die ungefähre Höhe des Pennys nach 7 Sekunden. t h A. 907 Fuß B. 912 Fuß C. 923 Fuß D. 928 Fuß Bonus: Finden Sie die Lösung(en) für die quadratische Gleichung unten. x ( x 8) 3( x+ 2) = 2( x+ 9) Gina Wilson, 2013 73 DANKE, dass Sie sich für dieses Produkt entschieden haben! Bitte schauen Sie in meinem Laden vorbei und lassen Sie mich wissen, wie es gelaufen ist! (Indem Sie Feedback hinterlassen, verdienen Sie TpT-Credits für zukünftige Einkäufe!) BLEIBEN SIE IN VERBINDUNG! Blog: Pinterest: Facebook: CREDITS: Fonts provided by KevinandAmanda.com Frames provided by The Enlightened Elephant 2013 Gina Wilson, All Things Algebra Products by Gina Wilson (All Things Algebra) may be used by the purchaser for their classroom use only. All rights reserved. No part of this publication may be reproduced, distributed, or transmitted without the written permission of the author. This includes posting this product on the internet in any form, including classroom/personal websites or network drives. If you wish to share this product with your team or colleagues, you may purchase additional licenses from my store at a discounted price! 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 Quadratic Equations in Vertex Form What is vertex form? y = a(x h) 2 + k where (h, k) is the vertex of the parabola. How do we convert this back to standard form standard form? Use! 93 94 95 Name: Unit 8: Quadratic Equations Date: Bell: Homework 4: Solving Quadratics by Factoring (Day 1) ** This is a 2-page document! ** 96 97 98 99 100 101 102 Writing Quadratic Equations by Identifying the Roots! 1 y = ( )( ) x + 4 x y = x + 2x y = ( )( ) x - 7 x y = x - 15x y = ( )( ) x + 8 x y = x + 11x y = ( )( ) x + 1 x y = x - 4x - 5 103 104 105 Name: Unit 8: Quadratic Equations Date: Bell: Homework 6: Solving Quadratics by The Quadratic Formula ** This is a 2-page document! ** 106 107 108 109 110 111 112 113 114 115 116 117 Name: Unit 8: Quadratic Equations Date: Bell: Homework 9: Solving Quadratics Review (All Methods) ** This is a 2-page document! ** 118 119 120 121 122 123 Name: Unit 8: Quadratic Equations Date: Bell: Homework 10: Quadratic Word Problems ** This is a 2-page document! ** 124 125 126 127 Name: Date: Bell: Unit 8: Quadratic Equations Homework 11: Linear and Quadratic Models ** This is a 2-page document! ** 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143
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