# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=(x+5)^2-1?

Mar 7, 2017

#### Explanation:

This is a typical quadratic equation in vertex form.

In a vertex form of equation such as $y = a {\left(x - h\right)}^{2} + k$

axis of symmetry is $x - h = 0$

and maxima is at $x = h$ and $y = k$, if $a < 0$ and minima is at $x = h$ and $y = k$, if $a > 0$

In $y = {\left(x + 5\right)}^{2} - 1$

axis of symmetry is $x + 5 = 0$

and as $a = 1$, we have a minima at $x = - 5$ and $y = - 1$ i.e. $\left(- 5 , - 1\right)$

The graph appears as follows.
graph{(x+5)^2-1 [-9.625, 0.375, -2.66, 2.34]}