Question

How do you find the vertex of a parabola `y=2x^2 -12x+23`?

Answer 1

The easiest way is (probably) to convert the given equation into vertex form.
The vertex is at `(3,5)`

Explanation:

Vertex form of a parabola is
`color(white)("XXXX")` `y =m(x-a)^2+b` with its vertex as `(a,b)`

`y = 2x^2-12x+23`
`color(white)("XXXX")`extract the `m`
`y = 2(x^2-6x) +23`
`color(white)("XXXX")`complete the square
`y = 2(x^2-6x+9) + 23 -2(9)`
`color(white)("XXXX")`simplify into vertex form
`y=2(x-3)^2 + 5`

Since this is in vertex form, we can read the vertex directly from the equation as `(3,5)`