To find the x-intercepts of the quadratic equation \(y = x^2 + 3x + 8\), we need to set \(y\) to zero and solve for \(x\):
\[ 0 = x^2 + 3x + 8 \]
We can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \(a = 1\), \(b = 3\), and \(c = 8\). Let's calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 - 4ac = 3^2 - 4(1)(8) = 9 - 32 = -23 \]
Since the discriminant is negative (\(-23\)), this indicates that there are no real solutions for \(x\). Therefore, this quadratic does not intersect the x-axis.
Conclusion:
The correct response is: There is no x-intercept.