Quadratic functions can be written in vertex form, or
This is especially useful because the vertex of the function is found at the point (h, k).
We can find this form by completing squares, for instance, let y be:
we can see that this equation is equal to
because
and
However, in this form, we can see that the first 3 terms are a perfect square, that is
hence,
If we define
we have that
the constant a arise when you have a leading term different from 1 in x^2.