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(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
To solve the quadratic function f(x) = -x^2 + 10x, we need to find the values of x where the function equals zero. This involves solving the quadratic equation -x^2 + 10x = 0.
Step 1: Factor out the common term x: x(-x + 10) = 0.
Step 2: Set each factor equal to zero and solve for x:
x = 0 (from x = 0)
-x + 10 = 0 (from -x + 10 = 0)
Step 3: Solve the second equation for x:
-x + 10 = 0
-x = -10
x = 10
So the solutions to the quadratic equation are x = 0 and x = 10.
Alternatively, you can use the quadratic formula to solve any quadratic equation in the form ax^2 + bx + c = 0. The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a. For this particular quadratic function, a = -1, b = 10, and c = 0. Plugging these values into the quadratic formula will yield the same solutions x = 0 and x = 10.