To find a point that lies on the parabola described by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the \( x \) values from the provided options into the equation and see if we get the corresponding \( y \) values.
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For \( x = -3 \): \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \] Thus, the point \( (-3, -55) \) is on the parabola.
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For \( x = -6 \): \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] The point \( (-6, 206) \) is not on the parabola since \( y \) should be -226, not 206.
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For \( x = -6 \) again (to check the point \( (-6, 8) \)): As calculated above, it is not valid, since we found \( y = -226 \) when \( x = -6 \).
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For \( x = -3 \) again (it was already checked): The valid point is \( (-3, -55) \).
Thus, from your options, the correct point that generates a position on the parabola defined by the equation is:
\[ (-3, -55) \]