Question

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

Answer 1

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]}