Question

select the correct answer.

what is the standard form of this function?

(f(x) = -(x - 4)^2 + 2)

(\bigcirc) (f(x) = x^2 + 8x - 14)

(\bigcirc) (f(x) = -x^2 + 4x - 30)

(\bigcirc) (f(x) = -x^2 + 8x - 14)

(\bigcirc) (f(x) = x^2 + 4x - 30)

Explanation:

Expand the squared binomial

$$ (x - 4)^2 = x^2 - 8x + 16 $$

Apply the negative sign

$$ -(x - 4)^2 = -(x^2 - 8x + 16) = -x^2 + 8x - 16 $$

Add the constant term

$$ f(x) = (-x^2 + 8x - 16) + 2 = -x^2 + 8x - 14 $$

Answer:

• (A) \(f(x) = x^2 + 8x - 14\)
• (B) \(f(x) = -x^2 + 4x - 30\)
• (C) \(f(x) = -x^2 + 8x - 14\) (Correct answer)
• (D) \(f(x) = x^2 + 4x - 30\)