Question

What are the y- and x-intercepts for `f(x) = 2x^3 - 6x^2 - 20x`?

Answer 1

`y` intercept at `(0,0)`
`x` intercepts at `(-2,0), (0,0), (5,0)`

Explanation:

graph{2x^3-6x^2-20x [-22.8, 22.81, -11.4, 11.4]}

The y-intercept is 0, because the function hasn't specified a y-intercept in. (if it did, it wouldn't have an x-coefficient)

For the x-intercepts, find where the y coordinate is 0. In this case, it's (-2,0), (0,0) and (5,0). These are also the solutions to the equation:
`0=2x^3 - 6x^2 - 20x`

As `2x^3-6x^2-20x=2x(x^2-3x-10)=2x(x-5)(x+2)`

and hence `f(x)=0` for `x=-2,0` and `5`.
Hope this helps.