Transformations of Quadratic Functions Assignment

Which of the following transforms the graph of y=x2 to the graph of y=x2-7?

Translation 7 units down

Enter the values of h and k so that y = x2 + 6x + 10 is in vertex form. y = (x + ___)2 + ___

y = (x + 3)2 + 1

Write the equation of the function whose graph is shown. y = (x + ___ )2 + ___

y = (x - 5)2 + 3 (usually put -5 on it because you have to change the sign)

1. The vertex of the graph of y = (x - 1)2 - 5 is 2. The vertex of the graph of y = -4(x + 3)2 + 2 is

A. (1,-5) B. (-3,2)

Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9? Check all of the boxes that apply. A. The vertex is (1, -9). B. The graph opens upward. C. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. D. The graph is steeper than the graph of f(x) = x2. E. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

B, D, E

A ball is thrown straight up from a height of 3 ft with a speed of 32 ft/s. Its height above the ground after x seconds is given by the quadratic function y = -16x2 + 32x + 3. Explain the steps you would use to determine the path of the ball in terms of a transformation of the graph of y = x2.

Sample Response: Complete the square to get the equation in vertex form with a = -16, h = 1, and k = 19. The path is a reflection over the x-axis and narrower. It is also translated right 1 unit and up 19 units.

Which of following is the graph of y = -(x + 1)2 -3?

The Third Graph

The graph of y = 5x2 is _______________, the graph of y = x2.

narrower than and opens in the SAME direction as

Which of the following transforms y=x2 to the graph of y=(x+5)2?

A translation 5 units to the left

Complete the statements below that show y = x2 + 2x - 1 being converted to vertex form. 1. Form a perfect-square trinomial. y = x2 + 2x + ___ − 1 − ___ 2. Factor the perfect-square trinomial in y = (x2 + 2x + 1) − 1− 1. y = (x + ___ )2 - 1 - 1 3. Simplify. y = (x + 1)2 - ___

A. y = x2 + 2x + 1 − 1 − 1 B. y = (x + 1)2 − 1 − 1 C. y = (x + 1)2 - 2

The graph of y = -0.2x2 is _______________, the graph of y = x2.

wider than and opens in the OPPOSITE direction of

Complete the statements below that show y = 8x2 + 32x + 17 being converted to vertex form. Factor out the leading coefficient. y = 8(x2 + 4x) + 17 1. Form a perfect-square trinomial. y = 8(x2 + 4x + ____) + 17 + ____ 2. Write in vertex form. y = 8(x + ____)2 + ____

A. y = 8(x2 + 4x + 4) + 17 -32 (changing the sign) B. y = 8(x + 2)2 -15 (changing the sign)

1. To obtain the graph of y = (x - 8)2, shift the graph of y = x2 2. To obtain the graph of y = x2 - 6, shift the graph of y = x2

A. right, 8 B. down, 6