Graph the quadratic y=x2+3x+8

Question

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

There is no x-intercept.
There is no x -intercept.

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

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

−1.5

Answer 1

To find the x-intercepts of the quadratic equation \(y = x^2 + 3x + 8\), we need to set \(y\) to zero and solve for \(x\):

\[ 0 = x^2 + 3x + 8 \]

We can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here, \(a = 1\), \(b = 3\), and \(c = 8\). Let's calculate the discriminant (\(b^2 - 4ac\)):

\[ b^2 - 4ac = 3^2 - 4(1)(8) = 9 - 32 = -23 \]

Since the discriminant is negative (\(-23\)), this indicates that there are no real solutions for \(x\). Therefore, this quadratic does not intersect the x-axis.

Conclusion:

The correct response is: There is no x-intercept.