Standard (vertex) form of a parabola

Question

Find the standard form of the parabola with the

vertex: (2,3) and directrix: y=0

Answer 1

vertex (2,3), directrix y=0

it's an upward opening parabola with focus (2,6), vertex midway between focus and directrix

y = a(x-2)^2 +3, plug in any other parabola point to solve for "a" such as (8,6)

6 = 36a +3

a = 1/12

y = (1/12)(x-2)^2 + 3