To determine which table of ordered pairs matches the given parabola \( y = -14x^2 + 3x - 6 \), we can evaluate the equation at various x-values and calculate the corresponding y-values. Let’s check the ordered pairs from the options provided and see if any match the outputs from the equation.
Step 1: Calculate y-values for selected x-values
I will choose x-values and compute the corresponding y-values using the parabola equation.
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For \( x = -2 \): \[ y = -14(-2)^2 + 3(-2) - 6 = -14(4) - 6 - 6 = -56 - 6 - 6 = -68 \]
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For \( x = -1 \): \[ y = -14(-1)^2 + 3(-1) - 6 = -14(1) - 3 - 6 = -14 - 3 - 6 = -23 \]
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For \( x = 0 \): \[ y = -14(0)^2 + 3(0) - 6 = -0 - 0 - 6 = -6 \]
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For \( x = 1 \): \[ y = -14(1)^2 + 3(1) - 6 = -14(1) + 3 - 6 = -14 + 3 - 6 = -17 \]
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For \( x = 2 \): \[ y = -14(2)^2 + 3(2) - 6 = -14(4) + 6 - 6 = -56 + 6 - 6 = -56 \]
Step 2: Check the provided ordered pairs
Let's compare these computed values of y:
- \( x = -2 \): \( y = -68 \)
- \( x = -1 \): \( y = -23 \)
- \( x = 0 \): \( y = -6 \)
- \( x = 1 \): \( y = -17 \)
- \( x = 2 \): \( y = -56 \)
Response Comparison
Let's break down each response you provided:
- Response 1: \((-2, -6), (-6, -10), (-10, -6)\) - Not matching.
- Response 2: \((2, -1), (6, 3), (10, -1)\) - Not matching.
- Response 3: \((0, -1), (-4, -5), (-8, -1)\) - Not matching.
- Response 4: \((4, -4), (2, -30), (-4, -1)\) - Not matching.
None of the provided tables of ordered pairs match with the calculated y-values from the parabola equation \( y = -14x^2 + 3x - 6 \).
Conclusion
Based on the calculations and the pairs given, it seems like there might be an error in the provided ordered pairs—they do not correspond to the values of y calculated from the parabola equation.