# How do you graph the quadratic function and identify the vertex and axis of symmetry for y=x^2-2x-1?

Feb 12, 2018

Vertex: $\left(1 , - 2\right)$
Axis of Symmetry: $x = 1$

#### Explanation:

You first convert to vertex form:

$y = a {\left(x - h\right)}^{2} + k$ with $\left(h , k\right)$ being the vertex. To get to this, you have to complete the square.

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

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

Since the vertex is $\left(h , k\right)$, then the vertex here is $\left(1 , - 2\right)$.

The axis of symmetry is just the x-coordinate of the vertex or $x = - \frac{b}{2 a}$ in $y = a {x}^{2} + b x + c$:

$x = 1$ is the axis of symmetry.