Graph the quadratic y=x2+3x+8

Question

. What is the x-intercept(s)?(1 point)
Responses

(0,8)
left parenthesis 0 comma 8 right parenthesis

−1.5
negative 1.5

(−1.5,5.75)
left parenthesis negative 1.5 comma 5.75 right parenthesis

There is no x-intercept.

Answer 1

To find the x-intercepts of the quadratic function \(y = x^2 + 3x + 8\), we need to determine when \(y = 0\): \[ x^2 + 3x + 8 = 0 \] We can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \(a = 1\), \(b = 3\), and \(c = 8\).

1. Calculate the discriminant: \[ b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23 \]

Since the discriminant is negative (\(-23\)), this means the quadratic has no real roots. Therefore, there are no x-intercepts.

So, the correct response is: There is no x-intercept.