To determine which of the coordinate pairs is a point on the parabola given by the equation \( y = -4x^2 - 53x - 56 \), we can substitute the x-coordinates from each pair into the equation and check if the resulting y-coordinate matches that of the point.
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For \((-1, -7)\): \[ y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -7 \] This point does satisfy the equation.
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For \((-4, -56)\): \[ y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92 \] This point does not satisfy the equation.
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For \((-4, 220)\): \[ y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = 92 \] This point does not satisfy the equation.
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For \((-1, 13)\): \[ y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -7 \] This point does not satisfy the equation.
Thus, the only point that satisfies the equation \( y = -4x^2 - 53x - 56 \) is \((-1, -7)\).
Answer: (-1, -7)
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