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):
[tex]2x^3 - 4x^2 = 0[/tex]
[tex]x^2(2x - 4) = 0[/tex]
Here we can apply the Zero Product Property to find [tex]x^2 = 0[/tex] and [tex]2x - 4 = 0[/tex] separately.
[tex]x^2 = 0[/tex]
[tex]x = 0[/tex]
AND
[tex]2x - 4 = 0[/tex]
[tex]2x = 4[/tex]
[tex]x = 2[/tex]
The x-intercepts are located at (0, 0) and (2, 0).
y-intercept (where x = 0):
[tex]y = 2(0)^3 - 4(0)^2[/tex]
[tex]y = 0[/tex]
The y-intercept is located at (0, 0).
