Find the x and y Intercepts y=2x^3-4x^2

Problem

y=2*x3−4*x2

Solution

1. Find the y-intercept by setting x=0 and solving for y

y=2*(0)3−4*(0)2

y=0

2. Find the x-intercepts by setting y=0 and solving for x

0=2*x3−4*x2

3. Factor out the greatest common factor from the right side of the equation.

0=2*x2*(x−2)

4. Apply the Zero Product Property by setting each factor equal to zero.

2*x2=0

x−2=0

5. Solve for x in each equation to find the x-coordinates of the intercepts.

x=0

x=2

Final Answer

x-intercepts: *(0,0),(2,0); y-intercept: *(0,0)

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