Question
Graph the quadratic y=x2+3x+8. What is the x-intercept(s)?(1 point)
Responses
−1.5
negative 1.5
There is no x-intercept.
There is no x -intercept.
(−1.5,5.75)
left parenthesis negative 1.5 comma 5.75 right parenthesis
(0,8)
Responses
−1.5
negative 1.5
There is no x-intercept.
There is no x -intercept.
(−1.5,5.75)
left parenthesis negative 1.5 comma 5.75 right parenthesis
(0,8)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the x-intercepts of the quadratic equation \( y = x^2 + 3x + 8 \), we need to set \( y = 0 \) and solve for \( x \).
The equation becomes:
\[
0 = x^2 + 3x + 8
\]
To determine the x-intercepts, we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
In this case, \( a = 1 \), \( b = 3 \), and \( c = 8 \).
Calculating 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 solutions for \( x \), indicating that there are no x-intercepts.
Thus, the correct response is:
**There is no x-intercept.**
The equation becomes:
\[
0 = x^2 + 3x + 8
\]
To determine the x-intercepts, we can use the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
In this case, \( a = 1 \), \( b = 3 \), and \( c = 8 \).
Calculating 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 solutions for \( x \), indicating that there are no x-intercepts.
Thus, the correct response is:
**There is no x-intercept.**
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