Question

question 3 of 10
what are the x-intercepts of the graph of the function below?
y = x² + 3x - 28

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

Explanation:

Step1: Recall x-intercept definition

To find x-intercepts, set \( y = 0 \), so solve \( x^{2}+3x - 28=0 \).

Step2: Factor the quadratic

Factor \( x^{2}+3x - 28 \). We need two numbers that multiply to \(-28\) and add to \(3\). The numbers are \(7\) and \(-4\) (since \(7\times(-4)=-28\) and \(7 + (-4)=3\)). So, \(x^{2}+3x - 28=(x + 7)(x - 4)\).

Step3: Solve for x

Set each factor equal to zero:

• \(x + 7 = 0\) gives \(x=-7\)
• \(x - 4 = 0\) gives \(x = 4\)

So the x-intercepts are \((-7,0)\) and \((4,0)\).

Answer:

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