Question

The graph of `y=(2x -4)(x+ 4)` is a parabola in the plane. How do you find the standard and vertex form?

Answer 1

The vertex form is `y=2((x+1)^2-9)`

Explanation:

Expand the equation
`y=(2x-4)(x+4)=2x^2+4x-16`
Then complete the squares for `x^2+2x`
`y=2(x^2+2x-8)=2(x^2+2x+1-8-1)`
`y=2((x+1)^2-9)`
So the line of symmetry has equation `x=-1`
and the vertex is at `(-1,-18)`
graph{2(x^2)+4x-16 [-40, 40, -20, 20]}