How do you get the equation of a parabola given line of symmetry and 2 points?

Question

A parabola, with axis of symmetry the y-axis, passes through each pair of points (2,9) and (3,14). With this information, how do I determine the equation of this parabola? Thanks!

Answer 1

The general equation of a parabola having axis of symmetry as the y-axis, is

x² = ay+b with its center at (0,-b/a)

It passes through each points (2,9) and (3,14).

∴ 2² = 9a+b ⇒ 9a+b = 4

and

3² = 14a+b ⇒ 14a+b = 9

∴ a = 1 and b = -5

The equation is x² = y-5