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).