To find the x-intercept(s) of the quadratic equation \(y = x^2 + 3x + 8\), we set \(y\) to zero and solve for \(x\):
\[ 0 = x^2 + 3x + 8 \]
To solve this quadratic equation, we can use the quadratic formula:
\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \]
where \(a = 1\), \(b = 3\), and \(c = 8\). First, we calculate the discriminant (\(b^2 - 4ac\)):
\[ b^2 - 4ac = 3^2 - 4(1)(8) = 9 - 32 = -23 \]
Since the discriminant is negative (\(-23\)), this means the quadratic does not cross the x-axis, and therefore there are no x-intercepts.
The correct response is:
There is no x-intercept.