Question

which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)?
(0,6)
(0,-6)
(6,0)
(-6,0)

Explanation:

Step1: Recall x-intercept definition

An x - intercept of a function \(y = f(x)\) is a point where \(y=0\), i.e., the point is of the form \((x,0)\). So we can eliminate the options \((0,6)\) and \((0, - 6)\) since their \(y\) - coordinate is not 0.

Step2: Solve for x when \(f(x)=0\)

Given \(f(x)=(x + 6)(x - 3)\), set \(f(x)=0\). Then, by the zero - product property, if \(ab = 0\), either \(a = 0\) or \(b = 0\). So we have two equations:

• Case 1: \(x+6=0\), which gives \(x=-6\).
• Case 2: \(x - 3=0\), which gives \(x = 3\).

So the x - intercepts of the function are \((-6,0)\) and \((3,0)\). Among the given options, \((-6,0)\) is an x - intercept.

Answer:

D. \((-6,0)\) (assuming the options are labeled as A. \((0,6)\), B. \((0,-6)\), C. \((6,0)\), D. \((-6,0)\))