If 3 and 5 are roots of the quadratic function f(x) , find f(2)

If 3 and 5 are roots of the quadratic function f(x) , find 
f(2)

First we need to determine the function
f(x):

We know that:

if x1 and x2 are
roots for the function, then ( x-x1) and ( x-x2) are factors of the
function:

Then we conclude that ( x-3) and (x -5) are factors of
f(x):

==> f(x) = (x-3) (
x-5)

Let us expand the
brackets:

==> f( x) = x^2 - 3x - 5x +
15

==> f(x) = x^2 - 8x + 15

Now
that we found f(x) we will calculate f(2) by substituting with x=
2:

==> f(2) = 2^2 - 8*2 +
15

==> f(2) = 4 - 16 +
15

==> f(2) =
3