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Answered

Which function in vertex form is equivalent to f(x) = x2 + 8 – 16x?


A.f(x) = (x – 8)2 – 56

B.f(x) = (x – 4)2 + 0

C.f(x) = (x + 8)2 – 72

D.f(x) = (x + 4)2 – 32

Verified Answer :

meerkat18

f(x) = x² + 8 - 16x

I'll rearrange it using y and x.

y = x² - 16x + 8
y - 8 = x² - 16x
y - 8 + 64 = x² - 16x + 64
y + 56 = (x-8)²
y = (x-8)² - 56

(x - 8)(x - 8) = x(x-8) - 8(x-8) = x² - 8x -8x + 64 = x² - 16x + 64

Choice A.) f(x) = (x-8)² - 56

xero099

By completing the square, the function in vertex form f(x) = (x - 8)² - 56 is equivalent to the function in standard form f(x) = x² + 8 - 16 · x. (Correct choice: A)

How to determine the vertex of the quadratic function by algebraic means

In this question we must transform a quadratic function in standard form into vertex form. An analytical approach is completing the square, which consists in transforming part of the polynomial into a perfect square trinomial. Now we proceed to present the procedure:

1) x² + 8 - 16 · x     Given

2) x² - 16 · x + 8    Commutative property

3) x² - 16 · x + 64 - 56     Modulative property/Existence of additive inverse/Definition of addition

4) (x - 8)² - 56     Associative property/Perfect square trinomial/Result

By completing the square, the function in vertex form f(x) = (x - 8)² - 56 is equivalent to the function in standard form f(x) = x² + 8 - 16 · x. (Correct choice: A)

To learn more on quadratic functions: https://brainly.com/question/5975436

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