To determine which point is on the parabola defined by the equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-values from the answer choices into the equation and see if the corresponding y-values match.
Let's evaluate each option:
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Option A: (-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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Option B: (-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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Option C: (-3, 323) The calculation for \( (-3, -55) \) revealed that the corresponding y-value is \( -55 \). Therefore, \( (-3, 323) \) cannot be on the parabola as the y-coordinate does not match.
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Option D: (-6, 8) \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] This point is also not on the parabola.
The only point from the options provided that lies on the parabola \( y = -6x^2 + 3x + 8 \) is A. (-3, -55).