# What is the axis of symmetry and vertex for the graph p(x)=(x+5)^2-3?

Sep 3, 2017

The vertex is at $\left(- 5 , - 3\right)$, and the axis of symmetry is at $x = - 5$.

#### Explanation:

This quadratic function is written in "vertex form", or $y = a {\left(x - h\right)}^{2} + k$, where $\left(h , k\right)$ is the vertex. This makes it really easy to see that, since $\left(x + 5\right) = \left(x - h\right)$, $h = - 5$. Remember to change the sign of $h$ when you see a quadratic in this form.
Since the ${x}^{2}$ term is positive, this parabola opens upward.

The axis of symmetry is just an imaginary line that goes through the vertex of a parabola where you would fold if you folded the parabola in half, with one side on top of the other.

Since that would be a vertical line through $\left(- 5 , - 3\right)$, the axis of symmetry is $x = - 5$.