Question
Graph the quadratic y=x2+3x+8 . What is the x-intercept(s)?(1 point)
Responses
(−1.5,5.75)
left parenthesis negative 1.5 comma 5.75 right parenthesis
There is no x-intercept.
There is no x -intercept.
(0,8)
left parenthesis 0 comma 8 right parenthesis
−1.5
Responses
(−1.5,5.75)
left parenthesis negative 1.5 comma 5.75 right parenthesis
There is no x-intercept.
There is no x -intercept.
(0,8)
left parenthesis 0 comma 8 right parenthesis
−1.5
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the x-intercepts of the quadratic function \( y = x^2 + 3x + 8 \), we need to set \( y = 0 \) and solve for \( x \):
\[
0 = x^2 + 3x + 8
\]
To solve this quadratic equation, we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Where \( a = 1 \), \( b = 3 \), and \( c = 8 \). First, we calculate the discriminant \( b^2 - 4ac \):
\[
b^2 - 4ac = 3^2 - 4(1)(8) = 9 - 32 = -23
\]
Since the discriminant is negative (\(-23\)), this means there are no real x-intercepts.
Therefore, the correct answer is:
**There is no x-intercept.**
\[
0 = x^2 + 3x + 8
\]
To solve this quadratic equation, we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Where \( a = 1 \), \( b = 3 \), and \( c = 8 \). First, we calculate the discriminant \( b^2 - 4ac \):
\[
b^2 - 4ac = 3^2 - 4(1)(8) = 9 - 32 = -23
\]
Since the discriminant is negative (\(-23\)), this means there are no real x-intercepts.
Therefore, the correct answer is:
**There is no x-intercept.**
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.