Write the quadratic function $f ( x ) = - x ^ { 2 } + 10 x - 18$ in standard form.
A) $f ( x ) = - ( x + 7 ) ^ { 2 } - 5$
B) $f ( x ) = - ( x + 5 ) ^ { 2 } + 7$
C) $f ( x ) = ( x - 5 ) ^ { 2 } - 7$
D) $f ( x ) = - ( x - 5 ) ^ { 2 } + 7$
E) $f ( x ) = ( x - 7 ) ^ { 2 } - 5$

Question

Write the quadratic function $f ( x ) = - x ^ { 2 } + 10 x - 18$ in standard form. 
A) $f ( x ) = - ( x + 7 ) ^ { 2 } - 5$
B) $f ( x ) = - ( x + 5 ) ^ { 2 } + 7$
C) $f ( x ) = ( x - 5 ) ^ { 2 } - 7$
D) $f ( x ) = - ( x - 5 ) ^ { 2 } + 7$
E) $f ( x ) = ( x - 7 ) ^ { 2 } - 5$

Quizplus · Accepted Answer

To convert the quadratic function from vertex form to standard form, we need to expand the square and simplify:
\begin{align*} f(x) & = -(x-5)^2 + 7 \ & = -x^2 + 10x - 25 + 7 \ & = -x^2 + 10x - 18 \end{align*}
So the standard form is $f(x) = -x^2 + 10x - 18$, which matches choice D.

Write the Quadratic Function f(x)=−x2+10x−18f ( x ) = - x ^ { 2 } + 10 x - 18f(x)=−x2+10x−18

Write the Quadratic Function $f ( x ) = - x ^ { 2 } + 10 x - 18$