To determine which of the given coordinate pairs is a point on the parabola defined by the equation \( y = -4x^2 - 53x - 56 \), we can substitute the \( x \)-values from the coordinate pairs into the equation and see if the resulting \( y \)-value matches the \( y \)-value from the coordinate pair.
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Check the point \((-4, -56)\): \[ y = -4(-4)^2 - 53(-4) - 56 \] \[ = -4(16) + 212 - 56 \] \[ = -64 + 212 - 56 = 92 \quad (\text{not } -56) \]
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Check the point \((-1, -7)\): \[ y = -4(-1)^2 - 53(-1) - 56 \] \[ = -4(1) + 53 - 56 \] \[ = -4 + 53 - 56 = -7 \quad (\text{matches } -7) \]
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Check the point \((-4, 220)\): \[ y = -4(-4)^2 - 53(-4) - 56 \] (We calculated this earlier and found it to be 92, not 220.) \[ = 92 \quad (\text{not } 220) \]
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Check the point \((-1, 13)\): \[ y = -4(-1)^2 - 53(-1) - 56 \] (We calculated this earlier and found it to be -7, not 13.) \[ = -7 \quad (\text{not } 13) \]
The only coordinate pair that is a point on the parabola is \((-1, -7)\).