Question

1. javier wants to graph the quadratic function shown p(x) = (x + 4)(x + 7). at what points does the graph of the function intersect the x-axis?

a. (4, 0) and (7, 0)
b. (-4, 0) and (7, 0)
c. (-4, 0) and (-7, 0)
d. (4, 0) and (-7, 0)

Explanation:

Step1: Find x-intercepts

To find where the graph intersects the x - axis, set \( p(x)=0 \). So, we have the equation \((x + 4)(x + 7)=0\).

Step2: Solve for x

Using the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \).

• If \( x+4 = 0 \), then \( x=-4 \).
• If \( x + 7=0 \), then \( x=-7 \).

The x - intercepts (points where the graph intersects the x - axis) are \((-4,0)\) and \((-7,0)\) because when \( x=-4 \) or \( x = - 7 \), \( y=p(x)=0\).

Answer:

C. \((-4, 0)\) and \((-7, 0)\)