Question
Malik is graphing a parabola given by the equation y=−14x2+3x−6
. Which table of ordered pairs would match this parabola?(1 point)
Responses
x-value y-value
2 −1
6 3
10 −1
x -value y -value 2 negative 1 6 3 10 negative 1
x-value y-value
−2
−6
−6
−10
−10
−6
x -value y -value negative 2 negative 6 negative 6 negative 10 negative 10 negative 6
x-value y-value
4 −4
2 −3
0 −4
x -value y -value 4 negative 4 2 negative 3 0 negative 4
x-value y-value
0 −1
−4
−5
−8
−1
x -value y -value 0 negative 1 negative 4 negative 5 negative 8 negative 1
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. Which table of ordered pairs would match this parabola?(1 point)
Responses
x-value y-value
2 −1
6 3
10 −1
x -value y -value 2 negative 1 6 3 10 negative 1
x-value y-value
−2
−6
−6
−10
−10
−6
x -value y -value negative 2 negative 6 negative 6 negative 10 negative 10 negative 6
x-value y-value
4 −4
2 −3
0 −4
x -value y -value 4 negative 4 2 negative 3 0 negative 4
x-value y-value
0 −1
−4
−5
−8
−1
x -value y -value 0 negative 1 negative 4 negative 5 negative 8 negative 1
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Answers
Answered by
GPT-4o mini
To determine which table of ordered pairs corresponds to the parabola given by the equation \( y = -14x^2 + 3x - 6 \), we can plug in the x-values from each response into the equation and calculate the corresponding y-values.
Let's evaluate the equation at various x-values based on the options provided:
1. **For x = 2**:
\[
y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56
\]
2. **For x = 6**:
\[
y = -14(6)^2 + 3(6) - 6 = -14(36) + 18 - 6 = -504 + 18 - 6 = -492
\]
3. **For x = 10**:
\[
y = -14(10)^2 + 3(10) - 6 = -14(100) + 30 - 6 = -1400 + 30 - 6 = -1376
\]
Next, we should try evaluating the pairs in the next responses:
4. **For x = -2**:
\[
y = -14(-2)^2 + 3(-2) - 6 = -14(4) - 6 - 6 = -56 - 6 - 6 = -68
\]
5. **For x = -6**:
\[
y = -14(-6)^2 + 3(-6) - 6 = -14(36) - 18 - 6 = -504 - 18 - 6 = -528
\]
6. **For x = -10**:
\[
y = -14(-10)^2 + 3(-10) - 6 = -14(100) - 30 - 6 = -1400 - 30 - 6 = -1436
\]
7. **For x = 4**:
\[
y = -14(4)^2 + 3(4) - 6 = -14(16) + 12 - 6 = -224 + 12 - 6 = -218
\]
8. **For x = 2** (again):
\[
y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56
\]
9. **For x = 0**:
\[
y = -14(0)^2 + 3(0) - 6 = 0 - 0 - 6 = -6
\]
10. **For x = 0 (another check)**:
\[
y = -14(0) + 3(0) - 6 = -6
\]
Now we summarize and compare results for pairs with the calculated y-values:
After checking values manually, it seems that none of the x-values in the first couple of tables produced outputs close to those seen in response pairs. The third option (x-values: 4, 2, 0) gives y-values that aren't aligning to our calculated expectations with potential legitimate outputs.
As such, I'd recommend recalibrating values through raw calculations or verifying criteria before concluding.
If we were to plot checked outputs and correlate existing pairs, further conclusions could be resolved distinctly.
Thus, it seems like the values from all the tables do not yield pairs that match the curve of the parabola displayed from the original question directly.
I hope this summary helps determine matching values effectively! Would you like additional clarity?
Let's evaluate the equation at various x-values based on the options provided:
1. **For x = 2**:
\[
y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56
\]
2. **For x = 6**:
\[
y = -14(6)^2 + 3(6) - 6 = -14(36) + 18 - 6 = -504 + 18 - 6 = -492
\]
3. **For x = 10**:
\[
y = -14(10)^2 + 3(10) - 6 = -14(100) + 30 - 6 = -1400 + 30 - 6 = -1376
\]
Next, we should try evaluating the pairs in the next responses:
4. **For x = -2**:
\[
y = -14(-2)^2 + 3(-2) - 6 = -14(4) - 6 - 6 = -56 - 6 - 6 = -68
\]
5. **For x = -6**:
\[
y = -14(-6)^2 + 3(-6) - 6 = -14(36) - 18 - 6 = -504 - 18 - 6 = -528
\]
6. **For x = -10**:
\[
y = -14(-10)^2 + 3(-10) - 6 = -14(100) - 30 - 6 = -1400 - 30 - 6 = -1436
\]
7. **For x = 4**:
\[
y = -14(4)^2 + 3(4) - 6 = -14(16) + 12 - 6 = -224 + 12 - 6 = -218
\]
8. **For x = 2** (again):
\[
y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56
\]
9. **For x = 0**:
\[
y = -14(0)^2 + 3(0) - 6 = 0 - 0 - 6 = -6
\]
10. **For x = 0 (another check)**:
\[
y = -14(0) + 3(0) - 6 = -6
\]
Now we summarize and compare results for pairs with the calculated y-values:
After checking values manually, it seems that none of the x-values in the first couple of tables produced outputs close to those seen in response pairs. The third option (x-values: 4, 2, 0) gives y-values that aren't aligning to our calculated expectations with potential legitimate outputs.
As such, I'd recommend recalibrating values through raw calculations or verifying criteria before concluding.
If we were to plot checked outputs and correlate existing pairs, further conclusions could be resolved distinctly.
Thus, it seems like the values from all the tables do not yield pairs that match the curve of the parabola displayed from the original question directly.
I hope this summary helps determine matching values effectively! Would you like additional clarity?