Question

How do you write `y = 2x^2-12x+11` into vertex form?

Answer 1

The general vertex form for a quadratic is
`y = m(x-a)+b` where `(a,b)` is the vertex.

`y=2x^2-12x+11`
`color(white)("XXXX")`extract the `m`
`y=2(x^2-6x) +11`
`color(white)("XXXX")`complete the square
`y=2(x^2-6x+9) +11 -18`
`color(white)("XXXX")`simplify to vertex form
`y=2(x-3)^2 + (-7)`
`color(white)("XXXX")`with the vertex at `(3,-7)`