y = a(x - h)² + k is the vertex form of an equation of a parabola with vertex (h,k)
We get the coordinates of the vertex of parabola from that form: (h, k)
We also know if the parabola goes up or down: a>0 or a<0
We can tell how many roots has the equation:
(a>0 and q>0) or (a<0 and q<0) ⇒ no roots
a≠0 and q=0 ⇒ one root: x₀=p
(a>0 and q<0) or (a<0 and q>0) ⇒ two roots
We can also determine the roots (if they exist):
a(x - h)² + k = 0
a(x - h)² = - k
(x - h)² = - k/a
x - h = √[-k/a] ∨ x - h = - √[-k/a]
x = √[-k/a] + h ∨ x = - √[-k/a] + h
Usually you use this form to find the equation of parabola when you have got given the vertex and some other point from that parabola.