Transformations of Quadratic Functions / Assignment

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

1, -5 / -3, 2

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

1, 1 / 1 / 2

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

1, 5, 3

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

3, 1

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 Form a perfect-square trinomial. y = 8(x2 + 4x + ) + 17 +

4, -32 / 2, -15

Which of the following transforms to the graph of ? a translation 5 units to the right a translation 5 units to the left a translation 5 units down a translation 5 units up Which of the following transforms the graph of to the graph of ? a translation 7 units to the right a translation 7 units to the left translation 7 units down a translation 7 units up

B / C

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. The vertex is (1, -9). The graph opens upward. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. The graph is steeper than the graph of f(x) = x2. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

B, D, E

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

C

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.

Complete the square to get the equation in vertex form witha = -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.

To obtain the graph of y = (x - 8)2, shift the graph of y = x2 updownleftright units. To obtain the graph of y = x2 - 6, shift the graph of y = x2 up downleftright units.

right, 8 / down, 6

The graph of y = -0.2x2 is X narrower than and opens in the same direction asX wider than and opens in the same direction asnarrower than and opens in the opposite direction of wider than and opens in the opposite direction of the graph of y = x2. The graph of y = 5x2 is narrower than and opens in the same direction aswider than and opens in the same direction asX narrower than and opens in the opposite direction ofwider than and opens in the opposite direction of the graph of y = x2.

wider than and opens in the opposite direction of the graph of / narrower than and opens in the same direction as