To determine if any of the given options is a point on the parabola described by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can evaluate the equation for each of the x-coordinates provided in the options, and check if the corresponding y-value matches.
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Option A: ( -6, 206) \[ y = -6(-6)^2 + 3(-6) + 8 \] \[ = -6(36) - 18 + 8 \] \[ = -216 - 18 + 8 \] \[ = -226 \quad (\text{not } 206) \]
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Option B: ( -3, 323) \[ y = -6(-3)^2 + 3(-3) + 8 \] \[ = -6(9) - 9 + 8 \] \[ = -54 - 9 + 8 \] \[ = -55 \quad (\text{not } 323) \]
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Option C: ( -6, 8) \[ y = -6(-6)^2 + 3(-6) + 8 \] \[ = -6(36) - 18 + 8 \] \[ = -216 - 18 + 8 \] \[ = -226 \quad (\text{not } 8) \]
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Option D: ( -3, -55) \[ y = -6(-3)^2 + 3(-3) + 8 \] \[ = -6(9) - 9 + 8 \] \[ = -54 - 9 + 8 \] \[ = -55 \quad (\text{matches -55}) \]
The point that satisfies the quadratic equation \( y = -6x^2 + 3x + 8 \) is D: (-3, -55).