Question

question 2 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: Set $y=0$ for x-intercepts

$x^2 + 3x - 28 = 0$

Step2: Factor the quadratic equation

We find two numbers that multiply to $-28$ and add to $3$: $7$ and $-4$.
$(x + 7)(x - 4) = 0$

Step3: Solve for $x$

Set each factor equal to 0:
$x + 7 = 0 \implies x = -7$
$x - 4 = 0 \implies x = 4$

Step4: Write intercept points

x-intercepts are $(-7, 0)$ and $(4, 0)$

Answer:

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