PreCalculus
posted by Amie on .
How do you solve this quadratic function?
f(x) = −x2 + 10x

All you have done is define f(x).
There is no "solution"
If you had written
f(x) = (any constant),
there would be a solution. 
Now, if you want to solve f(x) = 0,
f(x) = 2x(x5)
so, f=0 when either factor is zero. This is why we always set f(x) = 0 to solve for x, because the only time a product of numbers is zero is when one of them is zero. If we had 2x(x5) = 12, well, that doesn't help us because there are lots of numbers that multiply to equal 12. But if the product is zero, then one of the factors must be zero.
so, x=0 or x=5 will make f(x) = 0