To find the x-intercepts of the quadratic equation \(y = x^2 + 3x + 8\), we need to set \(y\) to 0 and solve for \(x\):
\[ 0 = x^2 + 3x + 8 \]
This is a standard quadratic equation of the form \(ax^2 + bx + c = 0\). Here, \(a = 1\), \(b = 3\), and \(c = 8\).
We can determine the x-intercepts using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
First, we need to calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23 \]
Since the discriminant is negative (\(-23\)), there are no real solutions to the equation, which means that there are no x-intercepts.
Therefore, the correct response is:
There is no x-intercept.