# What is the axis of symmetry and vertex for the graph y= -x^2 + 1?

Apr 8, 2017

Axis of symmetry is $x = 0$ ($y$-axis) and vertex is $\left(0 , 1\right)$

#### Explanation:

The axis of symmetry of $\left(y - k\right) = a {\left(x - h\right)}^{2}$ is $x - h = 0$ and vertex is $\left(h , k\right)$.

As $y = - {x}^{2} + 1$ can be written as

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

hence axis of symmetry is $x - 0 = 0$ i.e. $x = 0$ ($y$-axis) and vertex is $\left(0 , 1\right)$

graph{-x^2+1 [-10.29, 9.71, -6.44, 3.56]}

Note: The axis of symmetry of $\left(x - h\right) = a {\left(y - k\right)}^{2}$ is $y - k = 0$ and vertex is $\left(h , k\right)$.