To determine which of the given coordinate pairs is a point on the parabola defined by the equation \( y = -4x^2 - 53x - 56 \), we need to substitute the x-coordinate of each point into the equation and see if the resulting y-coordinate matches.
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For \((-1, 13)\): \[ y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -4 + 53 - 56 = -4 + (53 - 56) = -4 - 3 = -7 \quad \text{(not 13, so this point does not lie on the parabola)} \]
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For \((-1, -7)\): \[ y = -4(-1)^2 - 53(-1) - 56 = -4(1) + 53 - 56 = -4 + 53 - 56 = -4 + 53 - 56 = -4 - 3 = -7 \quad \text{(this matches, so this point lies on the parabola)} \]
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For \((-4, -56)\): \[ y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = -64 + 156 = 92 \quad \text{(not -56, so this point does not lie on the parabola)} \]
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For \((-4, 220)\): \[ y = -4(-4)^2 - 53(-4) - 56 = -4(16) + 212 - 56 = -64 + 212 - 56 = -64 + 156 = 92 \quad \text{(not 220, so this point does not lie on the parabola)} \]
Thus, the only point that lies on the parabola \( y = -4x^2 - 53x - 56 \) is:
\((-1, -7)\).
1 answer