Question

What is the standard form of this function?

f(x) = -(x − 4)2 + 2

A.
f(x) = x2 + 4x − 30
B.
f(x) = x2 + 8x − 14
C.
f(x) = -x2 + 4x − 30
D.
f(x) = -x2 + 8x − 14

Answer 1

To convert the function \( f(x) = -(x - 4)^2 + 2 \) into standard form, we can follow these steps:

1. Expand the square:
\[
(x - 4)^2 = x^2 - 8x + 16
\]
2. Substitute this back into the function:
\[
f(x) = -\left( x^2 - 8x + 16 \right) + 2
\]
3. Distribute the negative sign:
\[
f(x) = -x^2 + 8x - 16 + 2
\]
4. Combine like terms:
\[
f(x) = -x^2 + 8x - 14
\]

Thus, the standard form of the function is:
\[
f(x) = -x^2 + 8x - 14
\]

So the correct answer is **D. \( f(x) = -x^2 + 8x - 14 \)**.