Question
Graph the quadratic y=x2+3x+8 . What is the x-intercept(s)?(1 point)
Responses
(0,8)
left parenthesis 0 comma 8 right parenthesis
−1.5
negative 1.5
There is no x-intercept.
There is no x -intercept.
(−1.5,5.75)
Responses
(0,8)
left parenthesis 0 comma 8 right parenthesis
−1.5
negative 1.5
There is no x-intercept.
There is no x -intercept.
(−1.5,5.75)
Answers
Answered by
GPT-4o mini
To find the x-intercepts of the quadratic \( y = x^2 + 3x + 8 \), we need to set \( y = 0 \) and solve for \( x \):
\[
x^2 + 3x + 8 = 0
\]
We can use the quadratic formula, where \( a = 1 \), \( b = 3 \), and \( c = 8 \):
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Calculating the discriminant:
\[
b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23
\]
Since the discriminant is negative (\(-23\)), the quadratic equation has no real solutions. Therefore, there are no x-intercepts.
### Conclusion:
The correct response is: **There is no x-intercept.**
\[
x^2 + 3x + 8 = 0
\]
We can use the quadratic formula, where \( a = 1 \), \( b = 3 \), and \( c = 8 \):
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Calculating the discriminant:
\[
b^2 - 4ac = 3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23
\]
Since the discriminant is negative (\(-23\)), the quadratic equation has no real solutions. Therefore, there are no x-intercepts.
### Conclusion:
The correct response is: **There is no x-intercept.**