Question

What are the x-intercepts of the graph of the function below?
y=x2+4x-32
O (8, 0) and (-4, 0)
O (-8, 0) and (-4, 0)
• (-8, 0) and (4, 0)
• (8, 0) and (4, 0)

Answer 1

To find the x-intercepts of the function \( y = x^2 + 4x - 32 \), we need to set \( y \) to 0 and solve for \( x \):

\[
0 = x^2 + 4x - 32
\]

Now, we can solve this quadratic equation using the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \( a = 1 \), \( b = 4 \), and \( c = -32 \). Plugging in these values:

1. Calculate the discriminant:

\[
b^2 - 4ac = 4^2 - 4(1)(-32) = 16 + 128 = 144
\]

2. Now substitute into the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{144}}{2(1)} = \frac{-4 \pm 12}{2}
\]

This yields two solutions:

\[
x_1 = \frac{-4 + 12}{2} = \frac{8}{2} = 4
\]

\[
x_2 = \frac{-4 - 12}{2} = \frac{-16}{2} = -8
\]

Thus, the x-intercepts are:

\[
(4, 0) \quad \text{and} \quad (-8, 0)
\]

In conclusion, the correct option is:

• \( (-8, 0) \) and \( (4, 0) \)