Question

what are the x - intercepts of the parabola? y = x(x - 4)

Explanation:

Step1: Recall x - intercept definition

The x - intercepts of a function \(y = f(x)\) are found by setting \(y = 0\).

Step2: Set \(y = 0\) in the given equation

Given \(y=x(x - 4)\), set \(y = 0\). Then \(x(x - 4)=0\).

Step3: Use the zero - product property

If \(ab = 0\), then either \(a = 0\) or \(b = 0\). So, if \(x(x - 4)=0\), then \(x=0\) or \(x - 4=0\).

Step4: Solve for \(x\)

Solving \(x - 4=0\) gives \(x = 4\). The x - intercepts are the points \((0,0)\) and \((4,0)\).

Answer:

\((0,0)\) and \((4,0)\)