Completing the Square

Question 1

What is f(x) = x2 – 8x + 11 written in vertex form?f(x) = (x – 4)2 – 5f(x) = (x – 4)2 + 5f(x) = (x + 4)2 – 27f(x) = (x + 4)2 + 27

Revolt · Accepted Answer

A: f(x) = (x – 4)2 – 5

Question 2

What is h(x) = 7 + 10x + x2 written in vertex form?h(x) = (x – 25)2 – 18h(x) = (x – 5)2 + 32h(x) = (x + 5)2 – 18h(x) = (x + 25)2 + 32

Revolt · Accepted Answer

C: h(x) = (x + 5)2 – 18

Question 3

Determine the vertex form of g(x) = x2 + 2x – 1. Which graph represents g(x)?

Revolt · Accepted Answer

D: [Image: On a coordinate plane, a parabola opens up. It goe...]

Question 4

Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex? (1, 1)(1, 3)

Revolt · Accepted Answer

A:

Question 5

What is true about the function h(x) = x2 + 20x – 17? Check all that apply. The vertex of h is (–10, –117).The vertex form of the function is h(x) = (x + 20)2 – 17.The maximum value of the function is –17. To graph the function h, shift the graph of f(x) = x2 left 10 units and down 117 units.The axis of symmetry of function h is x = 20.

Revolt · Accepted Answer

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Question 6

The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function?(x – 11)2 + 58(x + 22)2 – 121(x + 7)2 – 47(x – 15)2 + 94

Revolt · Accepted Answer

C: (x + 7)2 – 47

Question 7

Explain the steps necessary to convert a quadratic function in standard form to vertex form.

Revolt · Accepted Answer

To convert a quadratic function from standard form to vertex form, you use the process of completing the square. First, focus on the first two terms (the x^2 and x terms). Create a perfect square trinomial by adding a zero pair. The value of this pair is found by taking half of the coefficient of the x-term and squaring it. One value is added to form the perfect square trinomial, which is then rewritten as a squared binomial, while the other value is combined with the original constant term outside of the binomial.

Question 8

Sample Response: A quadratic function in standard form is converted to vertex form by completing the square. The first two terms are used to create a perfect square trinomial after a zero pair is added. The zero pair is found by taking half of the x-term coefficient and squaring it. The original constant term and the negative value of the zero pair are then combined.

Revolt · Accepted Answer

A,B,C,D,E

Question 9

x2 + 8x + [___]

Revolt · Accepted Answer

16

Question 10

The vertex form of h(x) = x2 – 14x + 6 is h(x) = (x – [___])2 – [___].

Revolt · Accepted Answer

B: 7

Completing the Square Answers

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