Question

"Determine an equation of a quadratic function with x-intercepts of 2 and 6, that passes through the point (3, 12)"

Answer 1

I know how to do this question if I'm given the points of the vertex.. but in this case, it isn't. so..

Answer 2

start with
\[f(x)=a(x-2)(x-6)\] and then solve for \(a\) via \[f(3)=a(3-2)(3-6)=12\]

Answer 3

you get \[a\times 1\times -3=12\]
\[-3a=12\]
\[a=-4\] so your quadratic is
\[-4(x-2)(x-6)\] multiply out if you want

Answer 4

i get \(f(x)=-4 x^2+32 x-48\) but check my algebra

Answer 5

@satellite73, I got the same thing but the answer says it should be y = - 4 ( x - 4 )^2 + 16.

Answer 6

fine. i guess they wanted it in "vertex" form

Answer 7

Oh yeah, nevermind i got it. thank you so much!

Answer 8

convince yourself that they are equal

Answer 9

yw