Completing the Square Question

I am trying to model some data using the quadratic function

I am aware of the following points on my graph...
x-intercept(s) = -22.5 and +67.5
The vertex = (+22.5, +48)

Using the knowledge of these significant points on a quadratic graph, is there a way to work backwards from "Completing the Square" to be left with the equation in terms of ax²+bx+c. Or perhaps another method for calculating the parameters?

Feel free to try calculating the Quadratic equation yourself, but please leave your calculations. Thank you!

Since you dropped the y intercept from the previous question, you can do it the same way. take the 2 x roots:

(x+22.5)(x-67.5) = 0
from there, you can multiply both sides by an arbitrary number, say 'a', so:

a(x+22.5)(x-67.5) = a*0 = 0, so this is your equation:

y = a(x+22.5)(x-67.5), now plug in your vertex:

48 = a(22.5+22.5)(22.5-67.5) and solve for a.