Question

Find the x and y intercepts of y = 2x^3 - 4x^2 algebraically

Answer 1

The x-intercept is the place where y = 0 and the y-intercept is the point where x = 0. Using this information, we can substitute 0 in for x and y to find the intercepts.

x-intercepts (where y = 0):

`2x^3 - 4x^2 = 0`

`x^2(2x - 4) = 0`

Here we can apply the Zero Product Property to find
`x^2 = 0` and
`2x - 4 = 0` separately.

`x^2 = 0`

`x = 0`

AND

`2x - 4 = 0`

`2x = 4`

`x = 2`

The x-intercepts are located at (0, 0) and (2, 0).

y-intercept (where x = 0):

`y = 2(0)^3 - 4(0)^2`

`y = 0`

The y-intercept is located at (0, 0).