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.
-$$f ( x ) = x ^ { 2 } + x - 6$$
A) $f ( x ) = ( x + 1 ) ^ { 2 } - 6$
vertex: $( - 1 , - 6 )$
B) $f ( x ) = ( x - 1 ) ^ { 2 } - 4$
vertex: $( 1 , - 4 )$
C) $$\begin{array} { l }
f ( x ) = \left( x + \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 25 } { 4 } \
\text { vertex: } \left( - \frac { 1 } { 2 } , - \frac { 25 } { 4 } \right)
\end{array}$$
D) $$\begin{array} { l }
\mathrm { f } ( \mathrm { x } ) = \left( \mathrm { x } - \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 21 } { 4 } \
\text { vertex: } \left( \frac { 1 } { 2 } , - \frac { 21 } { 4 } \right)
\end{array}$$

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.
-$$f ( x ) = x ^ { 2 } + x - 6$$
A) $f ( x ) = ( x + 1 ) ^ { 2 } - 6$
vertex: $( - 1 , - 6 )$
B) $f ( x ) = ( x - 1 ) ^ { 2 } - 4$
vertex: $( 1 , - 4 )$
C) $$\begin{array} { l } 
f ( x ) = \left( x + \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 25 } { 4 } \
\text { vertex: } \left( - \frac { 1 } { 2 } , - \frac { 25 } { 4 } \right)
\end{array}$$
D) $$\begin{array} { l } 
\mathrm { f } ( \mathrm { x } ) = \left( \mathrm { x } - \frac { 1 } { 2 } \right) ^ { 2 } - \frac { 21 } { 4 } \
\text { vertex: } \left( \frac { 1 } { 2 } , - \frac { 21 } { 4 } \right)
\end{array}$$

Quizplus · Accepted Answer

To express $f(x) = x^2 + x - 6$ in vertex form, complete the square: $f(x) = (x^2 + x + \frac{1}{4}) - \frac{1}{4} - 6$, which simplifies to $f(x) = (x + \frac{1}{2})^2 - \frac{25}{4}$. The vertex form is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Thus, the vertex is $\left(-\frac{1}{2}, -\frac{25}{4}\right)$.

Express the Function in the Formss the Function in the Form