Question

Graph the quadratic y=x^2+3x+8
. What is the x-intercept(s)?(1 point)
Responses

-1.5
-1.5

(-1.5, 5.75)
(-1.5, 5.75)

(0, 8)
(0, 8)

There is no x-intercept.
There is no x-intercept.

Answer 1

To find the x-intercepts of the quadratic function \( y = x^2 + 3x + 8 \), we need to set \( y \) to 0 and solve for \( x \):

\[
0 = x^2 + 3x + 8
\]

This is a quadratic equation in standard form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = 3 \), and \( c = 8 \).

We can use the quadratic formula to solve for \( x \):

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

First, we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = 3^2 - 4(1)(8) = 9 - 32 = -23
\]

Since the discriminant is negative (\(-23\)), this means there are no real solutions. Therefore, the quadratic does not intersect the x-axis.

Based on this information, the correct response regarding the x-intercepts is:

**There is no x-intercept.**