Find a function whose graph is a parabola with vertex (4,9) and that passes through the point (5,12).How do you find this function??

Expert Answers
hala718 eNotes educator| Certified Educator

We will write the function in the vertex form:

`f(x)= a(x-h)^2 + k`  such that (h,k) is the vertex.

`==gt f(x)= a(x-4) + 9`

`` Now given the point (5,12) passes through the line.

`==gt f(5)= 12 `

`==gt f(5)= a(5-4)^2 +9 = 12 `

`==gt a + 9= 12 `

`==gt a = 12-9= 3 `

`==gt f(x)= 3(x-4)^2+ 9 `

`==gt f(x)= 3(x^2 -8x + 16)+ 9`

`` ==`gt f(x)= 3x^2 -24x + 57.`