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.
-$$f ( x ) = x ^ { 2 } - 3 x - 1$$
A) $f ( x ) = ( x - 5 ) ^ { 2 } - 1$
vertex: $( 5 , - 1 )$
B) $$\begin{array} { l }
f ( x ) = \left( x + \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 23 } { 4 } \
\text { vertex: } \left( - \frac { 3 } { 2 } , \frac { 23 } { 4 } \right)
\end{array}$$
C) $$\begin{array} { l }
f ( x ) = \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 13 } { 4 } \
\text { vertex: } \left( \frac { 3 } { 2 } , - \frac { 13 } { 4 } \right)
\end{array}$$
D) $f ( x ) = ( x + 3 ) ^ { 2 } + 17$
vertex: $( - 3,17 )$

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.
-$$f ( x ) = x ^ { 2 } - 3 x - 1$$
A) $f ( x ) = ( x - 5 ) ^ { 2 } - 1$
vertex: $( 5 , - 1 )$
B) $$\begin{array} { l } 
f ( x ) = \left( x + \frac { 3 } { 2 } \right) ^ { 2 } + \frac { 23 } { 4 } \
\text { vertex: } \left( - \frac { 3 } { 2 } , \frac { 23 } { 4 } \right)
\end{array}$$
C) $$\begin{array} { l } 
f ( x ) = \left( x - \frac { 3 } { 2 } \right) ^ { 2 } - \frac { 13 } { 4 } \
\text { vertex: } \left( \frac { 3 } { 2 } , - \frac { 13 } { 4 } \right)
\end{array}$$
D) $f ( x ) = ( x + 3 ) ^ { 2 } + 17$
vertex: $( - 3,17 )$

Quizplus · Accepted Answer

To express $f(x) = x^2 - 3x - 1$ in vertex form $f(x) = a(x - h)^2 + k$, complete the square: $f(x) = (x^2 - 3x + \frac{9}{4}) - \frac{9}{4} - 1 = (x - \frac{3}{2})^2 - \frac{13}{4}$. The vertex is $(\frac{3}{2}, -\frac{13}{4})$.

Express the Function in the Formss the Function in the Form