Question

How do you write the Vertex form equation of the parabola `y=x^2-2x+1`?

Answer 1

`y=1(x-1)^2+0`

Explanation:

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

Given:
`color(white)("XXX")y=x^2-2x+1`
and re-writing the expression on the left as a squared binomial:
`color(white)("XXX")y=(x-1)^2`
Note that some teachers would accept this as a final answer;
however to be technically complete we should include values for the `m` and `b` elements:
`color(white)("XXX")y=1(x-1)^2+0`