To determine which of the coordinate pairs is a point on the parabola defined by the equation \( y = -4x^2 - 53x - 56 \), we can substitute the x-coordinate of each pair into the equation and see if we obtain the corresponding y-coordinate.
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For \((-4, -56)\): \[ y = -4(-4)^2 - 53(-4) - 56 \] \[ y = -4(16) + 212 - 56 \] \[ y = -64 + 212 - 56 = 92 ; (\text{not } -56) \]
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For \((-1, -7)\): \[ y = -4(-1)^2 - 53(-1) - 56 \] \[ y = -4(1) + 53 - 56 \] \[ y = -4 + 53 - 56 = -7 ; (\text{matches}) \]
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For \((-4, 220)\): \[ y = -4(-4)^2 - 53(-4) - 56 \] \[ y = -4(16) + 212 - 56 \] \[ y = -64 + 212 - 56 = 92 ; (\text{not } 220) \]
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For \((-1, 13)\): \[ y = -4(-1)^2 - 53(-1) - 56 \] \[ y = -4(1) + 53 - 56 \] \[ y = -4 + 53 - 56 = -7 ; (\text{not } 13) \]
The only coordinate pair that is a point on the parabola \( y = -4x^2 - 53x - 56 \) is \((-1, -7)\).
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