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CW#18H: Compare Quadratic Functions & Solve by Graphing Honors Geometry Name: _____________________________ TP: ____ CRS Objectives Algebra Content XEI 605 Solve quadratic equations 4.3 Compare quadratic graphs in form y =ax2 + c with the parent quadratic function 4.4 Solve quadratic equations by graphing y = ax2 + bx + c y =ax2 + c Transformations - Quadratic functions can __________________ ( narrow) or ___________________ (wide) - Shift ___________ or ___________ - Reflect on the __________________________ Stretch (narrow) Shrink (wide) Shift up Shift down Reflection (sad face) 1) Which multiple choice option describes the correct transformation to the parent graph ( )? 2) How would the graph of the function y = x2 + 4 affected if the function were changed to y = x2 – 3? A. Shrink and shift down 1 units B. Stretch and shift down 3 units C. Stretch and reflection across the x-axis D. Shrink, shift down 3 units, and reflection across the x-axis E. Shrink and reflection across the x-axis A. The graph would shift 4 units up. B. The graph would shift 3 units down. C. The graph would shift 7 units down. D. The graph would shift 4 units to the right. E. The graph would shift 4 units down. 3) Describe the transformation of y = 5x2 – 4 to the parent function? 4) How would the graph of the function y = x2 -2 affected if the function were changed to y = x2 + 4? PUSH IT TO THE LIMIT. 5) Which multiple choice option describes the correct transformation to the parent graph ( )? 6) How would the graph of the function y = x2 – 2 affected if the function were changed to y = x2 + 1? A. Shrink and shift up 5 units B. Stretch and shift up 5 units C. Stretch and reflection across the x-axis D. Shrink, shift up 5 units, and reflection across the x-axis E. Stretch, shift up 5 units, and reflection across the xaxis 7) Describe the transformation of y = -x2 + 7 to the parent function? A. The graph would shift 1 unit up. B. The graph would shift 2 units down. C. The graph would shift 3 units down. D. The graph would shift 3 units to the right. E. The graph would shift 3 units up. 9) Describe the transformation of y = -2x2 – 4 to the parent function? 10) How would the graph of the function y = x2 – 6 affected if the function were changed to y = x2+ 2? 11) Describe the transformation of y = 6x2 + 8 to the parent function? 12) How would the graph of the function y = x2 + 1 affected if the function were changed to y = x2+ 5? 8) How would the graph of the function y = x2 + 2 affected if the function were changed to y = x2 – 5? PUSH IT TO THE LIMIT. Question: How do I solve quadratic equations by graphing? Step 1: Write the equation in standard form: _________________________ Step 2: Graph the function (following the steps from yesterday) to determine the __ - _______________. These values are called the “_________” or “_________” of a function, and are the solutions to the function. Quadratic Equation with TWO Quadratic Equation with ONE Quadratic equation with NO real solutions must have ___ solution must have ____ solution must have ___ x-intercepts. x-intercept. x-intercepts. Step 3: If solutions are found, check the solutions by substituting them into the ___________ _____________. 1) Solve x 2 2x 3 by graphing. a. Table: x 2) Find the zeros of the function: f (x) x 2 2x 1 b. Graph: a. Table: y x c. AOS: b. Graph: y d. Vertex: ( ___ , ___ ) circle one: max min c. AOS: d. Vertex: ( ___ , ___ ) circle one: max min e. Solutions: ___________________________ e. Solutions: ___________________________ PUSH IT TO THE LIMIT. 2 3) Find the roots of x 7 4 x . a. Table: x c. AOS: 4) Solve the equation by graphing. Label the vertex and axis of symmetry. b. Graph: y d. Vertex: ( ___ , ___ ) circle one: max min e. Solutions: ___________________________ 5) What are the roots of the function x 2 2 x 3 ? Label the vertex and axis of symmetry. 6) How many solutions does the quadratic equation have? Label the vertex and axis of symmetry. PUSH IT TO THE LIMIT. 7) The graph y x 2 4 x 5 is shown below. Which choice best describes the solution(s) to this equation? 8) The graph of y x 2 2x 3 is shown below. For what values of x does y 0 ? A. B. C. D. x 5 x 5 x 1 Both A and C 9) Use the graph to find the solution to the equation 11) Solve the equation by graphing. Label the vertex and axis of symmetry. A. B. C. D. x 1 and x 0 x 1 and x 3 x 3 and x 1 x 1 and x 3 10) Use the graph to find the solution to the equation 12) Solve the equation by graphing. Label the vertex and axis of symmetry. PUSH IT TO THE LIMIT. EXIT SLIP: 1) Find the zeros, if any, of 2 x 2 x 3 . a. Table: x c. AOS: NAME: ____________________________ 2) Describe the transformation of y = -½x2 – 1 to the parent function? b. Graph: y d. Vertex: ( ___ , ___ ) circle one: max min e. Solutions: ___________________________ PUSH IT TO THE LIMIT.