# How do you find the axis of symmetry, and the maximum or minimum value of the function y=2(x-2)^2-3?

May 30, 2017

Minimum

Vertex $\to \left(x , y\right) = \left(+ 2 , - 3\right)$

Axis of symmetry is $x = + 2$

#### Explanation:

If you multiply out the brackets the highest order term is $+ 2 {x}^{2}$

As this is positive the graph is of form $\cup$ thus we have a minimum/

Consider color(green)(y=2(xcolor(red)(-2))^2color(red)(-3)

Then Vertex $\to \left(x , y\right) = \left(\textcolor{red}{+ 2 , - 3}\right)$

So Axis of symmetry is $x = + 2$