To determine which of the provided coordinate pairs is a point on the parabola described by the equation \( y = 2x^2 - 24x - 15 \), we can substitute each \( x \) value from the pairs into the equation to see if the resulting \( y \) value matches.
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For the point (-11, 7): \[ y = 2(-11)^2 - 24(-11) - 15 \] \[ = 2(121) + 264 - 15 \] \[ = 242 + 264 - 15 = 491 \] Since \( 491 \neq 7 \), this point is not on the parabola.
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For the point (2, -47): \[ y = 2(2)^2 - 24(2) - 15 \] \[ = 2(4) - 48 - 15 \] \[ = 8 - 48 - 15 = -55 \] Since \( -55 \neq -47 \), this point is not on the parabola.
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For the point (11, -37): \[ y = 2(11)^2 - 24(11) - 15 \] \[ = 2(121) - 264 - 15 \] \[ = 242 - 264 - 15 = -37 \] Since \( -37 = -37 \), this point is on the parabola.
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For the point (2, -15): \[ y = 2(2)^2 - 24(2) - 15 \] This was calculated previously, yielding \( -55 \), so this point is also not on the parabola.
The only coordinate pair that is a point on the parabola is (11, -37).