Question

What is the vertex of `y=-2x^2 - 8x + 9`?

Answer 1

Vertex: `(-2,17)`

Explanation:

Our objective will be to convert the given equation into "vertex form":
`color(white)("XXX")y=m(x-a)^2+b` with vertex at `(a,b)`

Given
`color(white)("XXX")y=-2x^2-8x+9`

Extract the `m` factor
`color(white)("XXX")y=(-2)(x^2+4x)+9`

Complete the square:
`color(white)("XXX")y=(color(blue)(-2))(x^2+4xcolor(blue)(+4))+9color(red)(+8)`

Re-write the `x` expression as a binomial square
`color(white)("XXX")y=(-2)(x+2)^2+17`

Convert the squared binomial into form `(x-a)`
`color(white)("XXX")y=(-2)(x-(-2))+17`
which is the vertex form with vertex at `(-2,17)`
graph{-2x^2-8x+9 [-16.13, 15.93, 6, 22.01]}