Question

What is the vertex of `y=x^2-6x+15`?

Answer 1

Vertex is at `(3,6)`

Explanation:

The general vertex form of a parabola is
`color(white)("XXX")y=m(x-color(blue)(a))^2+color(blue)(b)` for a parabola with vertex at `(color(blue)(a,b))`

Converting `y=x^2-6x+15` into this form:

Complete the square:
`color(white)("XXX")y=x^2-6xcolor(red)(+3^2) + 15 color(red)(-3^2)`
Re-write as a squared binomial
`color(white)("XXX")y=(x-color(blue)(3))^2+color(blue)(6)`
which is in the vertex form (with `m=1`) for a parabola with vertex at `(color(blue)(3,6))`