# What is the axis of symmetry and vertex for the graph y = 3x^2 - 7x - 8?

##### 1 Answer
Aug 24, 2016

The axis of symmetry isthe line $x = \frac{7}{6}$
The vertex is $\left(\frac{7}{6} , - \frac{145}{12}\right)$

#### Explanation:

We know the shape of the graph , a parabola, in the same basic form as $y = {x}^{2}$ it will have a minimum point.
The minimum point is where the gradient of the curve is 0
Differentiate
$\frac{\mathrm{dy}}{\mathrm{dx}} = 6 x - 7$

$6 x - 7 = 0$ or the gradient is zero, when $x = \frac{7}{6}$

So the line $x = \frac{7}{6}$ is the line of symmetry.

Put this x value into the original equation to find the y coordinate of the vertex