# How do you find the vertex of a parabola y=-[x]^2+1?

Jul 18, 2015

The vertex is at color(red)((0,1).

#### Explanation:

$y = - {x}^{2} + 1$

The standard form of the equation for a parabola is

$y = a {x}^{2} + b x + c$, so

$a = - 1$, $b = 0$, $c = 1$

The $x$-coordinate is at $x = - \frac{b}{2 a} = - \frac{0}{2 \left(- 1\right)} = 0$

To find the $y$-coordinate of the vertex, substitute $x = 0$ into the equation to get

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

The vertex is at ($0 , 1$).

graph{-x^2+1 [-3, 3, -5, 2]}