Question

What is the x-intercept and y-intercept of the function `f(x) = x^3 - 3x^2 - 4x`?

Answer 1

y=0 and x=0,=1,4

Explanation:

Y-Intercept

In order to get the y-intercept, just plug in 0 as the x-value then you should get `0^3-3(0)-4(0)` or in other words, 0.

X-Intercept

Now here's where things start to get more complicated. Firstly, we should determine how many zeroes there are. We can see that from the x^3, there are 3 roots (because the power on the leading coefficient determines the amount of roots).

Then, we can see that all of the numbers in the equation have a x in common. We should take out that x in all the numbers in order to get `x(x^2-3x-4).`

Lastly, we expand the function in the middle with `x(x-4)(x+1).`
If we plug in 0 for the value, the x on the outside `(x(x-4)(x+1))` will become 0. Therefore, a zero is 0,0.

If we plug in 4, 4 would cancel out with x-4 to equal 0, and the whole equation would be multiplied by 0 to equal zero, therefore another 0 is 4,0.

Lastly, if we plug in -1, it would cancel with `x+1` to equal 0, which again would multiply the whole equation by 0 in order to equal 0. Therefore, the last zero is -1,0.