Question

Graph the quadratic y=x2+3x+8
𝑦
=
𝑥
2
+
3
𝑥
+
8
. What is the x-intercept(s)?(1 point)
Responses

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

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

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

−1.5
−
1.5
negative 1.5

Answer 1

To determine the x-intercepts of the quadratic equation \( y = x^2 + 3x + 8 \), we need to find the values of \( x \) for which \( y = 0 \). We can do this by solving the equation:

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

We can use the discriminant method to determine if there are any real x-intercepts. The discriminant (\( D \)) is given by the formula:

\[
D = b^2 - 4ac
\]

For the quadratic \( y = ax^2 + bx + c \):

- \( a = 1 \)
- \( b = 3 \)
- \( c = 8 \)

Plugging in these values:

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

Since the discriminant is negative (\( D < 0 \)), this indicates that there are no real solutions to the equation \( x^2 + 3x + 8 = 0 \). Therefore, the quadratic does not intersect the x-axis.

### Conclusion
The answer is: **There is no x-intercept.**