Question 8 of 15 Calculate the discriminant of the quadratic function $y=x^{2}+3 x+8$. 일. (Give an exact answer. Use symbolic notation and fractions where needed.) discriminant: What does the discriminant tell you about the zeros? The equation has one real zero. no real zeros. two real zeros.

Step 1 ：The discriminant of a quadratic function is given by the formula \(D = b^{2} - 4ac\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation. In this case, \(a = 1\), \(b = 3\), and \(c = 8\).

Step 2 ：The discriminant tells us about the nature of the roots of the quadratic equation. If \(D > 0\), the equation has two distinct real roots. If \(D = 0\), the equation has one real root. If \(D < 0\), the equation has no real roots.

Step 3 ：Let's calculate the discriminant for this equation. \(D = b^{2} - 4ac = 3^{2} - 4*1*8 = -23\)

Step 4 ：The discriminant is -23, which is less than 0. This means that the quadratic equation has no real roots.

Step 5 ：Final Answer: The discriminant of the quadratic function \(y=x^{2}+3 x+8\) is \(\boxed{-23}\). The equation has \(\boxed{no real zeros}\).