Question

Graph the quadratic y=x2+3x+8
. What is the x-intercept(s)?(1 point)
Responses

−1.5
negative 1.5

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

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

(0,8)

Answer 1

To find the x-intercepts of the quadratic function \( y = x^2 + 3x + 8 \), we need to set \( y = 0 \) and solve for \( x \):

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

Next, we can use the quadratic formula:

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

Where \( a = 1 \), \( b = 3 \), and \( c = 8 \). Plugging in these values gives:

\[
x = \frac{-3 \pm \sqrt{3^2 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}
\]

Calculating the discriminant:

\[
3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23
\]

Since the discriminant is negative (\( -23 \)), it indicates that there are no real x-intercepts.

Thus, the answer is:
**There is no x-intercept.**