Find the quadratic function that has the indicated vertex and whose graph passes through the given point.

Question

Vertex: (2,3) Point: (0,2)

I do not know how to do this! Please explain!! Thank You

Answer 1

Write it in vertex form

y = a(x-2)^2 + 3, the only thing we don't know is the a value
sub in the given point
2 = a(-2)^2 + 3
-1 = 4a
a = -1/4

so
y = (-1/4)(x-2)^2 + 3

expand it if you need it in general form