Answer
Axis of symmetry: $x= -\frac{1}{2}$
Vertex: $(-\frac{1}{2},-\frac{13}{2})$
Work Step by Step
$y = 6x^{2} + 6x - 5$
The standard form for a quadratic equation is
$y = ax^{2} + bx + c$ So a= 6, b= 6, and c= -5
Axis of symmetry:
The formula for axis of symmetry is
$x= \frac{-b}{2a}$
$x= \frac{-(6)}{2(6)}$
$x= \frac{-6}{12}$
$x= -\frac{1}{2}$
Vertex:
Plug in the x value of the axis of symmetry to find the y value of the vertex.
$y = 6x^{2} + 6x - 5$
$y = 6(-\frac{1}{2})^{2} + 6(-\frac{1}{2}) - 5$
$y= -\frac{13}{2}$
The vertex is $(-\frac{1}{2},-\frac{13}{2})$
