Question

Graph the quadratic y=x2+3x+8 . What is the x-intercept(s)?(1 point)
Responses

−1.5
negative 1.5

(0,8)
left parenthesis 0 comma 8 right parenthesis

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

(−1.5,5.75)

Answer 1

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

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

To find the x-intercepts, we can use the quadratic formula, which is given by:

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

For the equation \(x^2 + 3x + 8\):
- \(a = 1\)
- \(b = 3\)
- \(c = 8\)

Now substituting these values into the quadratic formula:

1. Calculate the discriminant (\(b^2 - 4ac\)):

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

Since the discriminant is negative (\(-23\)), there are no real solutions for \(x\). This means that the quadratic does not cross the x-axis, and therefore there are no x-intercepts.

Thus, the answer is:

**There is no x-intercept.**