Question

what are the x-intercepts of the graph of the function below?

y = x^2 + 3x - 28

Answer 1

To find the x-intercepts of the function \( y = x^2 + 3x - 28 \), we need to set \( y \) equal to 0 and solve for \( x \):

\[
0 = x^2 + 3x - 28
\]

This is a quadratic equation in the standard form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = 3 \), and \( c = -28 \).

We can solve this using the quadratic formula:

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

First, calculate the discriminant:

\[
b^2 - 4ac = 3^2 - 4(1)(-28) = 9 + 112 = 121
\]

Next, substitute the values into the quadratic formula:

\[
x = \frac{-3 \pm \sqrt{121}}{2(1)}
\]

\[
x = \frac{-3 \pm 11}{2}
\]

Now, we will find the two possible values for \( x \):

1.

\[
x = \frac{-3 + 11}{2} = \frac{8}{2} = 4
\]

2.

\[
x = \frac{-3 - 11}{2} = \frac{-14}{2} = -7
\]

Thus, the x-intercepts of the graph are:

\[
\boxed{4} \text{ and } \boxed{-7}
\]