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.
-$$f ( x ) = - x ^ { 2 } + x - 4$$
A) $f ( x ) = - ( x - 1 ) ^ { 2 } - 4$
vertex: $( 1 , - 4 )$
B) $$\begin{array} { l }
f ( x ) = - \left( x - \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 15 } { 4 } \
\text { vertex: } \left( \frac { 1 } { 2 } , - \frac { 15 } { 4 } \right)
\end{array}$$
C) $$\begin{array} { l }
f ( x ) = - \left( x + \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 19 } { 4 } \
\text { vertex: } : \left( - \frac { 1 } { 2 } , - \frac { 19 } { 4 } \right)
\end{array}$$
D) $f ( x ) = - ( x + 1 ) ^ { 2 } - 6$
vertex: $( - 1 , - 6 )$

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.
-$$f ( x ) = - x ^ { 2 } + x - 4$$
A) $f ( x ) = - ( x - 1 ) ^ { 2 } - 4$
vertex: $( 1 , - 4 )$
B) $$\begin{array} { l } 
f ( x ) = - \left( x - \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 15 } { 4 } \
\text { vertex: } \left( \frac { 1 } { 2 } , - \frac { 15 } { 4 } \right)
\end{array}$$
C) $$\begin{array} { l } 
f ( x ) = - \left( x + \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 19 } { 4 } \
\text { vertex: } : \left( - \frac { 1 } { 2 } , - \frac { 19 } { 4 } \right)
\end{array}$$
D) $f ( x ) = - ( x + 1 ) ^ { 2 } - 6$
vertex: $( - 1 , - 6 )$

Quizplus · Accepted Answer

To express the given function in the form $f(x) = a(x - h)^2 + k$, we complete the square. The original function is $f(x) = -x^2 + x - 4$. Completing the square involves factoring out the coefficient of $x^2$ (which is -1 in this case) from the first two terms and then adding and subtracting the square of half the coefficient of $x$ (which is $1/2$, so we add and subtract $(-1/2)^2 = 1/4$). This process results in the function being rewritten as $f(x) = -\left(x - \frac{1}{2}\right)^2 - \frac{15}{4}$, with the vertex at $\left(\frac{1}{2}, -\frac{15}{4}\right)$.

Express the Function in the Formss the Function in the Form