Question

what are the x - intercepts of the parabola? y = ½(x + 2)(x - 6) (-2,6) (2,0) and (-6,0) (-2,0) and (6,0) (½,0) and (-2,0) and (6,0)

Explanation:

Step1: Recall x - intercept definition

The x - intercepts of a function \(y = f(x)\) are found by setting \(y = 0\). So for \(y=\frac{1}{4}(x + 2)(x-6)\), we set \(y = 0\).

Step2: Solve the equation

If \(\frac{1}{4}(x + 2)(x - 6)=0\), then either \(x+2 = 0\) or \(x - 6=0\) (by the zero - product property: if \(ab = 0\), then \(a = 0\) or \(b = 0\)).
For \(x+2 = 0\), we get \(x=-2\). For \(x - 6=0\), we get \(x = 6\). The x - intercepts are the points \((-2,0)\) and \((6,0)\).

Answer:

\((-2,0)\) and \((6,0)\)