Parabola has a vertex4,5

Question

A parabola has a vertex (4,5) and goes through the point (1,23). Write the equation of the parabola in vertex form

Answer 1

First of all, this parabola with vertex at (4,5) going thru (1,23) could be opening either up or left. I will assume it is opening up.

y = a(x - h)^2 + k where (h,k) is the vertex

y + a(x - 4)^2 + 5

To find a we will put in the known point.

23 = a(1 - 4)^2 + 5

23 = a(-3)^2 + 5

23 = 9a + 5

a = 2

y = 2(x - 4)^2 + 5