Graph the quadratic y=x2+3x+8

Question

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

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

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

−1.5
−
1.5
negative 1.5

There is no x-intercept.

Answer 1

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

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

Next, to solve this quadratic equation, we can use the quadratic formula:

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

Here, \( a = 1 \), \( b = 3 \), and \( c = 8 \).

Calculating the discriminant:

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

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

Thus, the correct response is:

There is no x-intercept.