Lesson 7. Opening Exercise Warm Up 1. Without graphing, state the vertex for each of the following quadratic equations.
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1 : Further Explorations of Vertex Form, yy = aa(xx hh) + kk Opening Exercise Warm Up 1. Without graphing, state the vertex for each of the following quadratic equations. A. yy = (xx 5) + 3 B. yy = xx.5 C. yy = (xx + 4). Write a quadratic equation whose graph will have the given vertex. A. (1.9, 4) B. (0, 100) C., 3 : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.55 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
2 Explorat ory Challenge Your group will need: Quadratic Matching Game Cards 3. With your group, match four different aspects of a given quadratic function. There are cards for the vertex, equation in standard form, y-intercept and graph. Record your matches in the table below. Your graph should be a rough sketch, but put in at least 3 key points. Equation in Vertex Form Equation in Standard Form Vertex y-intercept Graph A. y= ( x ) B. y= ( x+ 5) 1 : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.56 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
3 Equation in Vertex Form Equation in Standard Form Vertex y-intercept Graph C. y= ( x+ 1) + 3 D. y= ( x 1) + 3 E. y= ( x 5) + 1 : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.57 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
4 Equation in Vertex Form Equation in Standard Form Vertex y-intercept Graph F. y= ( x+ ) + G. y= ( x+ 1) + : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.58 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
5 4. For each equation from Exercise 3, determine the axis of symmetry. Then draw the axis of symmetry on your graphs in Exercise 3. Equation in Vertex Form Axis of Symmetry A. B. C. D. E. F. G. y= ( x ) y= ( x+ 5) 1 y= ( x+ 1) + 3 y= ( x 1) + 3 y= ( x 5) + 1 y= ( x+ ) + y= ( x+ 1) + 5. Scott says that his tutor gave him an equation to find the axis of symmetry. If the equation is in standard b form f(x) = ax + bx + c, then the equation for the axis of symmetry is x =. Use the standard forms of a the equations from Exercise 3 to verify the axis of symmetry. (These are in no particular order.) Equation in Standard Form b Axis of Symmetry Using x = a A. B. C. D. E. F. G. y= x + x+ y= x + 10x+ 4 y= x 4x y= x 4x+ y= x + x+ 3 y= x x+ y= x 10x+ 6 : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.59 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
6 : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.60 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
7 Homework Problem Set 1. Find the vertex of the graphs of the following quadratic equations. A. yy = (xx 5) B. yy = (xx + 1) 8 For each problem below identify which equation satisfy the given conditions. In some cases there may only be one equation that works, while others have multiple equations that fulfill the requirements.. Vertex: (3, -) fx () = 3x + fx () = ( x 3) + fx () = ( x 3) + fx () = ( x 3) fx () = ( x 3) 3. Vertex: (1, 4); y-intercept: 5 fx () = ( x 1) + 4 fx () = x x+ 5 fx () = x + x+ 5 fx () = x 4x+ 5 fx () = ( x 1) y-intercept: 3 fx () = x + 3 fx () = x x+ 3 fx () = ( x 1) + 4 fx () = ( x+ 1) + 5 : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.61 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
8 5. Prove your results from Problem. (The equations are given at the right for your convenience.) For each graph below, state the vertex, axis of symmetry and write the equation of each function. 6. Vertex: 7. Vertex: Axis of Symmetry: Axis of Symmetry: 1 ( ) y = x 1 ( ) y = x 4 8. Write an equation of a quadratic function that has an axis of symmetry of x = 0. : Further Explorations of the Vertex Form, yy = aa(xx h) + kk Unit 8: Introduction to Quadratics & Their Transformations S.6 This work is derived from Eureka Math and licensed by Great Minds. 015 Great Minds. eureka-math.org This file derived from ALG I--TE
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