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 quadratic equation in standard form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = 3 \), and \( c = 8 \).
We can use the discriminant to determine if there are any real x-intercepts. The discriminant \( D \) is given by:
\[ D = b^2 - 4ac \]
Substituting the values:
\[ D = 3^2 - 4(1)(8) = 9 - 32 = -23 \]
Since the discriminant is negative (\( D < 0 \)), this means that the quadratic does not intersect the x-axis and there are no real x-intercepts.
Thus, the response to the question about the x-intercept is:
There is no x-intercept.