Write the quadratic function $f ( x ) = - x ^ { 2 } + 8 x - 8$ in standard form.
A) $f ( x ) = ( x - 8 ) ^ { 2 } - 4$
B) $f ( x ) = ( x - 4 ) ^ { 2 } - 8$
C) $f ( x ) = - ( x + 4 ) ^ { 2 } + 8$
D) $f ( x ) = - ( x + 8 ) ^ { 2 } - 4$
E) $f ( x ) = - ( x - 4 ) ^ { 2 } + 8$

Question

Quizplus · Accepted Answer

To write the quadratic function in standard form, complete the square. The given function is $f(x) = -x^2 + 8x - 8$. Factoring out the coefficient of $x^2$ (which is -1) from the first two terms gives $f(x) = -(x^2 - 8x) - 8$. To complete the square, add and subtract $(\frac{8}{2})^2 = 16$ inside the parenthesis, resulting in $f(x) = -(x^2 - 8x + 16) + 16 - 8$, which simplifies to $f(x) = -(x - 4)^2 + 8$.

Write the Quadratic Function f(x)=−x2+8x−8f ( x ) = - x ^ { 2 } + 8 x - 8f(x)=−x2+8x−8

Write the Quadratic Function $f ( x ) = - x ^ { 2 } + 8 x - 8$