To determine which table of ordered pairs matches the parabola given by the equation \( y = -14x^2 + 3x - 6 \), we will evaluate the equation for the x-values in each table and check if the calculated y-values match.
Given Equation:
\[ y = -14x^2 + 3x - 6 \]
Table 1:
x-value | y-value
0 | -1
-4 | -5
-8 | -1
Calculate:
- For \( x = 0 \): \[ y = -14(0)^2 + 3(0) - 6 = -6 \quad \text{(not -1)} \]
- For \( x = -4 \): \[ y = -14(-4)^2 + 3(-4) - 6 = -14(16) - 12 - 6 = -224 - 12 - 6 = -242 \quad \text{(not -5)} \]
- For \( x = -8 \): \[ y = -14(-8)^2 + 3(-8) - 6 = -14(64) - 24 - 6 = -896 - 24 - 6 = -926 \quad \text{(not -1)} \]
Table 2:
x-value | y-value
-2 | -6
-6 | -10
-10 | -6
Calculate:
- For \( x = -2 \): \[ y = -14(-2)^2 + 3(-2) - 6 = -14(4) - 6 - 6 = -56 - 6 - 6 = -68 \quad \text{(not -6)} \]
- For \( x = -6 \): \[ y = -14(-6)^2 + 3(-6) - 6 = -14(36) - 18 - 6 = -504 - 18 - 6 = -528 \quad \text{(not -10)} \]
- For \( x = -10 \): \[ y = -14(-10)^2 + 3(-10) - 6 = -14(100) - 30 - 6 = -1400 - 30 - 6 = -1436 \quad \text{(not -6)} \]
Table 3:
x-value | y-value
4 | -4
2 | -3
0 | -4
Calculate:
- For \( x = 4 \): \[ y = -14(4)^2 + 3(4) - 6 = -14(16) + 12 - 6 = -224 + 12 - 6 = -218 \quad \text{(not -4)} \]
- For \( x = 2 \): \[ y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56 \quad \text{(not -3)} \]
- For \( x = 0 \): \[ y = -14(0)^2 + 3(0) - 6 = -6 \quad \text{(not -4)} \]
Table 4:
x-value | y-value
2 | -1
6 | 3
10 | -1
Calculate:
- For \( x = 2 \): \[ y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56 \quad \text{(not -1)} \]
- For \( x = 6 \): \[ y = -14(6)^2 + 3(6) - 6 = -14(36) + 18 - 6 = -504 + 18 - 6 = -492 \quad \text{(not 3)} \]
- For \( x = 10 \): \[ y = -14(10)^2 + 3(10) - 6 = -14(100) + 30 - 6 = -1400 + 30 - 6 = -1376 \quad \text{(not -1)} \]
Conclusion:
None of the provided tables match the parabola described by the equation \( y = -14x^2 + 3x - 6 \). You may want to check the tables again or re-evaluate the values to find a match.