# What is the axis of symmetry and vertex for the graph y=x^2-7?

Jul 3, 2017

Axis of symmetry is $x = 0$ i.e. $y$-axis and vertex is $\left(0 , - 7\right)$.

#### Explanation:

A general equation of a parabola is $y = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is the vertex and $x - h = 0$ is the axis of symmetry.

Observe that we can write the given equation $y = {x}^{2} - 7$ as

$y = 1 \times {\left(x - 0\right)}^{2} - 7$

and hence while axis of symmetry is $x = 0$ i.e. $y$-axis and vertex is $\left(0 , - 7\right)$.

graph{(y-x^2+7)(x^2+(y+7)^2-0.02)=0 [-20, 20, -10, 10]}