You can put this solution on YOUR website! To get from vertex form
y= a(x-h)^2 + k
to standard form-
y=ax^2 + bx + c
Using Y = (X-1)^2 + 2 as an example.
First you expand (x-h)^2 to a quadratic
Y = (X-1)^2 + 2
Y = (x^2 - 2x + 1) + 2
Then you add the K value to the quadratic
Y = (x^2 - 2x + 1) + 2
Y = (x^2 - 2x + 3)
And then you're finished!