Find the Vertex of the Graph of the Quadratic Function $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x + \frac { 15 } { 2 }$

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
- $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } + 4 x + \frac { 15 } { 2 }$

A) Vertex: $\left( - 4 , - \frac { 1 } { 2 } \right)$
$x$ -intercepts: $( - 5,0 )$ and $( - 3,0 )$ ;
$y$ -intercept: $\left( 0 , \frac { 15 } { 2 } \right)$

B) Vertex: $\left( 4 , \frac { 1 } { 2 } \right)$ ;
$x$ -intercepts: $( 5,0 )$ and $( 3,0 )$ ;
$y$ -intercept: $\left( 0 , - \frac { 15 } { 2 } \right)$

C) Vertex: $\left( 4 , - \frac { 1 } { 2 } \right)$
$x$ -intercepts: $( 5,0 )$ and $( 3,0 )$ ;
$y$ -intercept $\left( 0 , \frac { 15 } { 2 } \right)$

D) Vertex: $\left( - 4 , \frac { 1 } { 2 } \right)$
$x$ -intercepts: $( - 5,0 )$ and $( - 3,0 )$ ;
$y \text {-intercept: }\left(0,-\frac{15}{2}\right)$