# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y = 2x^2 - 6x - 36?

Jul 25, 2017

The function has a minimum at $x = 1.5$

Axis of symmetry $x = 1.5$

#### Explanation:

Given -

$y = 2 {x}^{2} - 6 x - 36$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 4 x - 6$
$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = 4 > 0$
$\frac{\mathrm{dy}}{\mathrm{dx}} = 0 \implies 4 x - 6 = 0$
$x = \frac{6}{4} = 1.5$

At x=1.5; dy/dx=0;(d^2y)/(dx^2)>0

The function has a minimum at $x = 1.5$

Axis of symmetry $x = 1.5$

Graph -