6
Select the correct answer.
What is the standard form of this function?
\[
f(x)=-(x-4)^{2}+2
\]
A. $f(x)=-x^{2}+4 x-30$
B. $f(x)=-x^{2}+8 x-14$
C. $f(x)=x^{2}+8 x-14$
D. $f(x)=x^{2}+4 x-30$
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Answer
\(\boxed{f(x) = -x^2 + 8x - 14}\) is the standard form of the function.
Step 1 ：The standard form of a quadratic function is \(f(x) = ax^2 + bx + c\).
Step 2 ：To find the standard form of the given function, we need to expand the square and simplify the equation.
Step 3 ：Let's expand \((x - 4)^2\) to get \(x^2 - 8x + 16\).
Step 4 ：Substitute this into the function to get \(f(x) = - (x^2 - 8x + 16) + 2\).
Step 5 ：Simplify this to get \(f(x) = -x^2 + 8x - 14\).
Step 6 ：\(\boxed{f(x) = -x^2 + 8x - 14}\) is the standard form of the function.
