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Chapter 1: Problem 29

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$y=2 x^{3}-4 x^{2}$$

Short Answer

Expert verified
The x-intercepts of the equation \(y=2 x^{3}-4 x^{2}\) are at \(x = 0\) and \(x = 2\). The y-intercept is at \(y = 0\).

Step by step solution

01

Find the x-intercepts

Set \(y\) to zero and solve for \(x\). So, \(0=2 x^{3}-4 x^{2}\). To solve the equation, first factor out \(2x^{2}\) to get \(2x^{2}(x - 2) = 0\). Then you can set each factor equal to zero and solve for \(x\). Hence, \(x = 0\) or \(x = 2\).
02

Find the y-intercept

Set \(x\) to zero and solve for \(y\). So, \(y=2(0)^{3}-4(0)^{2} = 0.\) Hence, the y-intercept is \(y = 0\) as the line passes through the origin (0,0).

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