Question

How do you write `y= -4x^2+8x-1` into vertex form?

Answer 1

General vertex form for a parabolic equation is
`y=m(x-a)^2 +b`
where the vertex is at `(a,b)`

Given `y =-4x^2+8x-1`

Extract `m`
`y = (-4)(x^2-2x) -1`

Complete the square
`y=color(blue)((-4))(x^2-2xcolor(blue)(+1)) - 1 color(blue)(+4)`

`y= (-4)(x-1)+3`
is in vertex form (with the vertex at `(1,3)`)