To determine which of the given points lies on the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-coordinates of the points into the equation and see if the resulting y-value matches.
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Check point \( a (-3, -55) \): \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \] This point is on the parabola.
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Check point \( b (-3, 323) \): Using the previous calculation for \( x = -3 \), we know \( y = -55 \), not \( 323 \). So this point is not on the parabola.
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Check point \( c (-6, 206) \): \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] This point is not on the parabola.
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Check point \( d (-6, 8) \): Using the calculation for \( x = -6 \), we know \( y = -226 \), not \( 8 \). So this point is not on the parabola.
Therefore, the only point from the options you provided that lies on the parabola \( y = -6x^2 + 3x + 8 \) is point a (-3, -55).
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