Lesson 6. Opening Exercise 1. Without graphing, state the vertex for each of the following quadratic equations.
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1 : Further Exploration of Vertex Form, yy = aa(xx hh) + kk Opening Exercise 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 Exploration of the Vertex Form, yy = aa(xx h) + kk Unit 10: Introduction to Quadratics S.39 This file derived from ALG I--TE
2 Explorat ory Challenge Your group will need: Quadratic Matching Game Cards 3. With your group, you ll match four different aspects of a given quadratic function. There are vertex cards, equations in standard form, y-intercept cards and graph cards. Record your matches in the table below. Your graph should be a rough sketch. Equation in Vertex Form Equation in Standard Form Vertex y-intercept Graph A. y= ( x ) B. y= ( x+ 5) 1 C. y= ( x+ 1) + 3 : Further Exploration of the Vertex Form, yy = aa(xx h) + kk Unit 10: Introduction to Quadratics S.40 This file derived from ALG I--TE
3 Equation in Vertex Form Equation in Standard Form Vertex y-intercept Graph D. y= ( x 1) + 3 E. y= ( x 5) + 1 F. y= ( x+ ) + G. y= ( x+ 1) + : Further Exploration of the Vertex Form, yy = aa(xx h) + kk Unit 10: Introduction to Quadratics S.41 This file derived from ALG I--TE
4 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 Exploration of the Vertex Form, yy = aa(xx h) + kk Unit 10: Introduction to Quadratics S.4 This file derived from ALG I--TE
5 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 Exploration of the Vertex Form, yy = aa(xx h) + kk Unit 10: Introduction to Quadratics S.43 This file derived from ALG I--TE
6 5. Prove your results from Problem. (The equations are given at the right for your convenience.) : Further Exploration of the Vertex Form, yy = aa(xx h) + kk Unit 10: Introduction to Quadratics S.44 This file derived from ALG I--TE
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