To determine which of the given points lies on the parabola described by the equation \( y = -6x^2 + 3x + 8 \), we can substitute the \( x \)-coordinates of each point into the equation and see if the resulting \( y \)-value matches the \( y \)-coordinate of the point.
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For point (-3, -55): \[ y = -6(-3)^2 + 3(-3) + 8 \] \[ = -6(9) - 9 + 8 \] \[ = -54 - 9 + 8 \] \[ = -55 \] This point is on the parabola.
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For point (-6, 206): \[ y = -6(-6)^2 + 3(-6) + 8 \] \[ = -6(36) - 18 + 8 \] \[ = -216 - 18 + 8 \] \[ = -226 \] This point is not on the parabola.
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For point (-3, 323): We already calculated \( y \) for \( x = -3 \) and found it to be -55. So this point is not on the parabola.
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For point (-6, 8): \[ y = -6(-6)^2 + 3(-6) + 8 \] We already calculated this: \[ = -216 - 18 + 8 \] \[ = -226 \] This point is not on the parabola.
From the calculations, the only point that is on the parabola is (-3, -55).
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