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