Question

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

(-1.5, 5.75)
(-1.5, 5.75)

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

(0, 8)
(0, 8)

-1.5

Answer 1

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

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

Next, 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, this means that there are no real x-intercepts for this quadratic function.

Now let's look at the provided responses:

- (-1.5, 5.75)
- **There is no x-intercept.** (This one is correct)
- (0, 8)
- -1.5

The correct answer is **There is no x-intercept.**