To find the x-intercept(s) of the quadratic equation \( y = x^2 + 3x + 8 \), we need to set \( y = 0 \) and solve for \( x \):
\[ 0 = x^2 + 3x + 8. \]
This is a standard quadratic equation of the form \( ax^2 + bx + c \), where \( a = 1, b = 3, c = 8 \).
To find the x-intercepts, we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \]
Substituting in the values of \( a \), \( b \), and \( c \):
- Calculate the discriminant (\( b^2 - 4ac \)): \[ b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23. \]
Since the discriminant is negative (\(-23\)), it indicates that there are no real solutions and therefore no x-intercepts.
Thus, the correct response is:
There is no x-intercept.