To find the x-intercept(s) of the quadratic function \( y = x^2 + 3x + 8 \), we need to set \( y \) to 0 and solve for \( x \):
\[ 0 = x^2 + 3x + 8 \]
Next, we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 3 \), and \( c = 8 \).
Calculating the discriminant:
\[ b^2 - 4ac = 3^2 - 4(1)(8) = 9 - 32 = -23 \]
Since the discriminant is negative (-23), this means that there are no real roots, and thus there are no x-intercepts.
Therefore, the answer is:
There is no x-intercept.
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