Question

What is the standard form of this function? f(x) = -(x − 4)2 + 2 A. f(x) = -x2 + 8x − 14 B. f(x) = x2 + 4x − 30 C. f(x) = -x2 + 4x − 30 D. f(x) = x2 + 8x − 14

Answer 1

f(x) = -x² + 8x − 14

Answer 2

option A. f(x) = -x² + 8x − 14

Explanation:

The standard form of a quadratic equation in general is as following:

f(x) = ax² + bx + c.

Where a, b and c are constants and a ≠ 0.

So, for the given function:

f(x) = -(x − 4)² + 2

∴ f(x) = - (x-4) (x-4) + 2

∴ f(x) = - [ x(x-4) - 4(x-4) ] + 2

∴ f(x) = - ( x² - 4x -4x + 16 ) + 2

∴ f(x) = - ( x² - 8x + 16 ) + 2

∴ f(x) = -x² + 8x - 16 + 2

∴ f(x) = -x² + 8x - 14

So, the answer is option A. f(x) = -x² + 8x − 14