Graph the Quadratic Equation $y = 2 x ^ { 2 } + 2 x - 1$

Graph the quadratic equation. Identify the vertex and the intercepts.
- $y = 2 x ^ { 2 } + 2 x - 1$

A) Vertex: $\left( - \frac { 1 } { 2 } , - \frac { 3 } { 2 } \right)$
$x$ -intercepts: $\left( \frac { - 1 - \sqrt { 7 } } { 2 } , 0 \right) , \left( \frac { - 1 + \sqrt { 7 } } { 2 } , 0 \right)$
$y$ -intercept: $( 0 , - 1 )$

B) Vertex: $\left( \frac { 1 } { 2 } , - \frac { 3 } { 2 } \right)$
x-intercepts: $\left( \frac { 1 - \sqrt { 3 } } { 2 } , 0 \right) , \left( \frac { 1 + \sqrt { 3 } } { 2 } , 0 \right)$
$y$ -intercept: $( 0 , - 1 )$

C) Vertex: $\left( \frac { 1 } { 2 } , - \frac { 3 } { 2 } \right)$
x-intercepts: $\left( \frac { 1 - \sqrt { 7 } } { 2 } , 0 \right) , \left( \frac { 1 + \sqrt { 7 } } { 2 } , 0 \right)$
$y$ -intercept: $( 0 , - 1 )$

D) Vertex: $\left( - \frac { 1 } { 2 } , - \frac { 3 } { 2 } \right)$
x-intercepts: $\left( \frac { - 1 - \sqrt { 3 } } { 2 } , 0 \right) , \left( \frac { - 1 + \sqrt { 3 } } { 2 } , 0 \right)$
$\mathrm { y }$ -intercept: $( 0 , - 1 )$