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

f (x) = - x² + 8x - 14

option A. f (x) = - x² + 8x - 14

Step-by-step 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