Question

How do you find the vertex of a parabola `y = x^2 - 6x + 10`?

Answer 1

The vertex is at `(3,1)`

Explanation:

The vertex form of a parabola is
`color(white)("XXXX")` `m(x-a)^2+b` with a vertex at `(a,b)`

Converting `y = x^2-6x+10` into vertex form:
`color(white)("XXXX")`Note `m=1` and we can continue with the rest of the conversion.
`color(white)("XXXX")`Complete the square
`color(white)("XXXX")` `color(white)("XXXX")` `y= x^2-6x+9 + 1`
`color(white)("XXXX")` `color(white)("XXXX")` `y = (x-3)+1`

and we can simply read off the vertex coordinates.