# How do you find the axis of symmetry and vertex point of the function: y = x^2 − 1?

Oct 18, 2015

Rewrite in explicit vertex form and recognize it as a parabola in standard position.
Vertex:$\left(0 , - 1\right) \textcolor{w h i t e}{\text{XXXX}}$Axis of symmetry: $x = 0$

#### Explanation:

Vertex form of a parabola in standard position:
$\textcolor{w h i t e}{\text{XXXX}} y = m {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$
$\textcolor{w h i t e}{\text{XXXXXXXX}}$with vertex at $\left(a , b\right)$ and opening upward if $m > 0$

$y = {x}^{2} - 1$
can be written in explicit vertex form as
$\textcolor{w h i t e}{\text{XXXX}} y = 1 {\left(x - \textcolor{red}{0}\right)}^{2} + \textcolor{b l u e}{\left(- 1\right)}$
$\textcolor{w h i t e}{\text{XXXXXXXX}}$with vertex at $\left(\textcolor{red}{0} , \textcolor{b l u e}{- 1}\right)$

In standard position the axis of symmetry is a vertical line through the vertex; i.e. $x = \textcolor{red}{0}$