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

Jan 26, 2016

Maximum $y = 7$
Axis of symmetry $x = 3$

#### Explanation:

Given -

$y = - {x}^{2} + 6 x - 2$
Vertex -

$x = \frac{- b}{2 a} = \frac{- 6}{2 \times \left(- 1\right)} = \frac{- 6}{- 2} = 3$
$y = - {\left(3\right)}^{2} + 6 \left(3\right) - 2 = - 9 + 18 - 2 = 18 - 11 = 7$

$\left(3 , 7\right)$

Axis of symmetry -

$x = 3$

How to graph?
After finding the vertex, take a few points on either side of $x = 3$
Find the corresponding y values.
Graph them