Express the function in the formss the function in the form f(x) $$f ( x ) = a ( x - h ) ^ { 2 } + k$$ k a nd indicate the vertex.
-$$f ( x ) = - x ^ { 2 } + 15 x + 5$$
A) $$\begin{array} { l }
f ( x ) = - \left( x - \frac { 15 } { 2 } \right) ^ { 2 } + \frac { 245 } { 4 } \
\text { vertex: } \left( \frac { 15 } { 2 } , \frac { 245 } { 4 } \right)
\end{array}$$
B) $f ( x ) = - ( x - 15 ) ^ { 2 } + 5$
vertex: $( 15,5 )$
C) $f ( x ) = - ( x + 15 ) ^ { 2 } - 445$
vertex: $( - 15 , - 445 )$
D) $$\begin{array} { l }
f ( x ) = - \left( x + \frac { 15 } { 2 } \right) ^ { 2 } - \frac { 655 } { 4 } \
\text { vertex: } \left( - \frac { 15 } { 2 } , - \frac { 655 } { 4 } \right)
\end{array}$$

Question

Express the function in the formss the function in the form f(x) $$f ( x ) = a ( x - h ) ^ { 2 } + k$$ k a nd indicate the vertex.
-$$f ( x ) = - x ^ { 2 } + 15 x + 5$$
A) $$\begin{array} { l } 
f ( x ) = - \left( x - \frac { 15 } { 2 } \right) ^ { 2 } + \frac { 245 } { 4 } \
\text { vertex: } \left( \frac { 15 } { 2 } , \frac { 245 } { 4 } \right)
\end{array}$$
B) $f ( x ) = - ( x - 15 ) ^ { 2 } + 5$
vertex: $( 15,5 )$
C) $f ( x ) = - ( x + 15 ) ^ { 2 } - 445$
vertex: $( - 15 , - 445 )$
D) $$\begin{array} { l } 
f ( x ) = - \left( x + \frac { 15 } { 2 } \right) ^ { 2 } - \frac { 655 } { 4 } \
\text { vertex: } \left( - \frac { 15 } { 2 } , - \frac { 655 } { 4 } \right)
\end{array}$$

Quizplus · Accepted Answer

To express the given quadratic function in vertex form, complete the square. The vertex form is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. For the given function $f(x) = -x^2 + 15x + 5$, factor out the coefficient of $x^2$ (which is -1) from the first two terms and complete the square. The result is $f(x) = -(x - \frac{15}{2})^2 + \frac{245}{4}$, with the vertex at $\left(\frac{15}{2}, \frac{245}{4}\right)$.

Express the Function in the Formss the Function in the Form