To find the x-intercepts of the quadratic equation \( y = x^2 + 3x + 8 \), we need to determine where \( y = 0 \).
Setting the equation to zero:
\[ x^2 + 3x + 8 = 0 \]
Next, we can use the discriminant \( D = b^2 - 4ac \) to find the nature of the roots, where \( a = 1 \), \( b = 3 \), and \( c = 8 \):
\[ D = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23 \]
Since the discriminant is negative, this means there are no real solutions, and consequently, there are no x-intercepts.
Thus, the correct response regarding the x-intercept of the quadratic \( y = x^2 + 3x + 8 \) is:
There is no x-intercept.