To find the x-intercepts of the quadratic \( y = x^2 + 3x + 8 \), we need to set \( y = 0 \) and solve for \( x \):
\[ x^2 + 3x + 8 = 0 \]
We can use the quadratic formula, where \( a = 1 \), \( b = 3 \), and \( c = 8 \):
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Calculating the discriminant:
\[ b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23 \]
Since the discriminant is negative (\(-23\)), the quadratic equation has no real solutions. Therefore, there are no x-intercepts.
Conclusion:
The correct response is: There is no x-intercept.
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