Question

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

−1.5
negative 1.5

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)

Answer 1

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

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

This is a standard quadratic equation of the form \( ax^2 + bx + c \), where \( a = 1, b = 3, c = 8 \).

To find the x-intercepts, we can use the quadratic formula:

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

Substituting in the values of \( a \), \( b \), and \( c \):

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

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

Thus, the correct response is:

**There is no x-intercept.**