To determine which coordinate pair is a point on the parabola given by the equation \( y = -4x^2 - 53x - 56 \), we will substitute the \( x \)-value from each coordinate pair into the equation and see if we obtain the corresponding \( y \)-value.
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For the point (-4, -56): \[ y = -4(-4)^2 - 53(-4) - 56 \] \[ y = -4(16) + 212 - 56 \] \[ y = -64 + 212 - 56 \] \[ y = 92 \quad (\text{not } -56) \]
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For the point (-4, 220): \[ y = -4(-4)^2 - 53(-4) - 56 \] We already calculated this: \[ y = 92 \quad (\text{not } 220) \]
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For the point (-1, -7): \[ y = -4(-1)^2 - 53(-1) - 56 \] \[ y = -4(1) + 53 - 56 \] \[ y = -4 + 53 - 56 \] \[ y = -7 \quad (\text{this is correct!}) \]
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For the point (-1, 13): \[ y = -4(-1)^2 - 53(-1) - 56 \] We already calculated this: \[ y = -7 \quad (\text{not } 13) \]
So, the point that lies on the parabola is (-1, -7).
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