Transformations of Quadratic Functions

Question 1

Enter the values of h and k so that y = x2 + 6x + 10 is in vertex form. y = (x + ⇒ 3)2 +

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Part 2: 1

Question 2

Write in vertex form. y = 8(x + )2 +

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Part 1: 2; Part 2: -15

Question 3

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.

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The graph opens upward.; The graph is narrower than the graph of f(x) = x2.; The graph is the same as the graph of f(x) = 6x2 + 12x - 3.

Question 4

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

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Part 1: 4; Part 2: -32

Question 5

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

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right

Question 6

Which of the following transforms to the graph of ?

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a translation 5 units to the left

Question 7

The graph of y = –0.2x2 is the graph of y = x2.

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wider than and opens in the opposite direction of

Question 8

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

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-5; 3

Question 9

Explain the steps you would use to determine the path of the ball in terms of a transformation of the graph of y = x2.

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To determine the path of the ball, first complete the square to rewrite the quadratic equation in vertex form, y = a(x - h)^2 + k. For the equation y = -16(x - 1)^2 + 19, the transformations include a reflection across the x-axis and a vertical stretch that makes the graph narrower because a = -16. Additionally, identify the translations: the graph is shifted 1 unit to the right (h = 1) and 19 units up (k = 19).

Question 10

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

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Part 2: -5

Transformations of Quadratic Functions Answers

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