To determine which table of ordered pairs corresponds to the parabola given by the equation \( y = -14x^2 + x - 4 \), we will evaluate the function at various \( x \) values and find the corresponding \( y \) values.
Let's compute \( y \) for several \( x \) values:
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For \( x = 2 \): \[ y = -14(2^2) + (2) - 4 = -14(4) + 2 - 4 = -56 + 2 - 4 = -58 \]
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For \( x = 0 \): \[ y = -14(0^2) + 0 - 4 = -4 \]
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For \( x = -2 \): \[ y = -14(-2^2) + (-2) - 4 = -14(4) - 2 - 4 = -56 - 2 - 4 = -62 \]
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For \( x = -4 \): \[ y = -14(-4^2) + (-4) - 4 = -14(16) - 4 - 4 = -224 - 4 - 4 = -232 \]
Next, we can check against the provided pairs:
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First table:
- \( (2, -1) \)
- \( (6, 3) \)
- \( (10, -1) \)
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Second table:
- \( (2, -3) \)
- \( (0, -4) \)
- \( (-2, -7) \)
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Third table:
- \( (2, -6) \)
- \( (-6, -10) \)
- \( (-10, -6) \)
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Fourth table:
- \( (0, -1) \)
- \( (-4, -5) \)
- \( (-8, -1) \)
Comparing the computed values:
- For \( x = 2 \), we found \( y = -58 \), which does not match any pairs.
- For \( x = 0 \), we found \( y = -4 \), which matches the second table: \( (0, -4) \).
- For \( x = -2 \), we found \( y = -62 \), and for \( x = -4 \), we got \( y = -232 \), neither of which appear in the tables.
While none of the pairs match the computed points perfectly, the second table includes one known value.
Thus, the best match indicating one point is the second table:
\[ \begin{align*} x & : y \ 2 & : -3 \ 0 & : -4 \ -2 & : -7 \ \end{align*} \]
This is the closest option based on part of the results computed, even though it does not fully represent the parabola accurately for all mentioned values.