Question

How do you solve this quadratic function?
f(x) = −x2 + 10x

Answer 1

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.

Answer 2

Now, if you want to solve f(x) = 0,

f(x) = -2x(x-5)

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(x-5) = 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