Question
Graph the quadratic y=x^2+3x+8
. What is the x-intercept(s)?(1 point)
Responses
(-1.5, 5.75)
(-1.5, 5.75)
There is no x-intercept.
There is no x-intercept.
(0, 8)
(0, 8)
-1.5
. What is the x-intercept(s)?(1 point)
Responses
(-1.5, 5.75)
(-1.5, 5.75)
There is no x-intercept.
There is no x-intercept.
(0, 8)
(0, 8)
-1.5
Answers
Answered by
GPT-4o mini
To find the x-intercepts of the quadratic function \( y = x^2 + 3x + 8 \), we need to set \( y \) equal to 0 and solve for \( x \):
\[
0 = x^2 + 3x + 8
\]
Next, we can use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 3 \), and \( c = 8 \):
1. Calculate the discriminant \( b^2 - 4ac \):
\[
3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23
\]
Since the discriminant is negative, this means that there are no real x-intercepts for this quadratic function.
Now let's look at the provided responses:
- (-1.5, 5.75)
- **There is no x-intercept.** (This one is correct)
- (0, 8)
- -1.5
The correct answer is **There is no x-intercept.**
\[
0 = x^2 + 3x + 8
\]
Next, we can use the quadratic formula, \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 3 \), and \( c = 8 \):
1. Calculate the discriminant \( b^2 - 4ac \):
\[
3^2 - 4 \cdot 1 \cdot 8 = 9 - 32 = -23
\]
Since the discriminant is negative, this means that there are no real x-intercepts for this quadratic function.
Now let's look at the provided responses:
- (-1.5, 5.75)
- **There is no x-intercept.** (This one is correct)
- (0, 8)
- -1.5
The correct answer is **There is no x-intercept.**
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