How do you find the vertex of a quadratic equation y= -x^2 + 9?

1 Answer
Jun 9, 2016

Vertex at: (0,9)

Explanation:

The general explicit vertex form is
color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)
for a parabola with vertex at (color(red)(a),color(blue)(b))

The given equation: y=-x^2+9
can be converted into the explicit vertex form as
color(white)("XXX")y=color(green)(""(-1))(x-color(red)(0))^2+color(blue)(9)
for a parabola with vertex at (color(red)(0),color(blue)(9))

For verification purposes, here is the graph of the original equation:
graph{-x^2+9 [-12.96, 12.35, -2.49, 10.17]}