To determine which coordinate pair is a point on the parabola given by the equation \( y = 2x^2 - 24x - 15 \), we will substitute the \( x \)-value of each point into the equation and see if it yields the corresponding \( y \)-value.
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For the point \((-11, 7)\): \[ y = 2(-11)^2 - 24(-11) - 15 \] \[ = 2(121) + 264 - 15 \] \[ = 242 + 264 - 15 = 491 \] So, \((-11, 491)\) does not match \((-11, 7)\).
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For the point \((2, -47)\): \[ y = 2(2)^2 - 24(2) - 15 \] \[ = 2(4) - 48 - 15 \] \[ = 8 - 48 - 15 = -55 \] So, \((2, -55)\) does not match \((2, -47)\).
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For the point \((11, -37)\): \[ y = 2(11)^2 - 24(11) - 15 \] \[ = 2(121) - 264 - 15 \] \[ = 242 - 264 - 15 = -37 \] So, \((11, -37)\) matches correctly.
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For the point \((2, -15)\): \[ y = 2(2)^2 - 24(2) - 15 \] \[ = 8 - 48 - 15 = -55 \] So, \((2, -55)\) does not match \((2, -15)\).
From the calculations above, the only point that lies on the parabola \( y = 2x^2 - 24x - 15 \) is \((11, -37)\).