Question

1. marisol wants to graph the quadratic function shown. h(x) = (x - 6)(x + 1). at what points does the graph of the function intersect the x-axis?

a. (-6, 0) and (1, 0)
b. (6, 0) and (-1, 0)
c. (6, 0) and (1, 0)
d. (-6, 0) and (-1, 0)

Explanation:

Step1: Recall x - intercept rule

To find x - intercepts, set \(h(x)=0\), so \(0=(x - 6)(x + 1)\).

Step2: Solve for x

Using zero - product property: if \(ab = 0\), then \(a = 0\) or \(b = 0\).
Case 1: \(x-6 = 0\), then \(x=6\). So one point is \((6,0)\) (since \(y = 0\) on x - axis).
Case 2: \(x + 1=0\), then \(x=-1\). So the other point is \((-1,0)\).

Answer:

B. (6, 0) and (-1, 0)