Final answer:
To find the zeros of the function f(x) = -4x^3 - 2x^2 + 2x, set the function equal to zero and solve for x. The vertical intercept is the value of f(x) when x = 0.
Step-by-step explanation:
To find the zeros of the function f(x) = -4x^3 - 2x^2 + 2x, we set the function equal to zero and solve for x. Rearranging the equation, we get:
-4x^3 - 2x^2 + 2x = 0
Now, we can factor out an x: x(-4x^2 - 2x + 2) = 0
This gives us two possible solutions: x = 0 or -4x^2 - 2x + 2 = 0. To find the zeros of the quadratic equation, we can either factor it or use the quadratic formula.
The vertical intercept of the function is the value of f(x) when x = 0. Plugging in x = 0, we get:
f(0) = -4(0)^3 - 2(0)^2 + 2(0) = 0