To find a point on the parabola generated by the quadratic equation y = -6x^2 + 3x + 8, we can substitute a value for x into the equation to solve for y. Let's try each point and see which one satisfies the equation:
Point (-3, 323):
y = -6(-3)^2 + 3(-3) + 8
y = -6(9) - 9 + 8
y = -54 - 9 + 8
y = -55
This point does not satisfy the equation.
Point (-6, 8):
y = -6(-6)^2 + 3(-6) + 8
y = -6(36) - 18 + 8
y = -216 - 18 + 8
y = -226
This point does not satisfy the equation.
Point (-6, 206):
y = -6(-6)^2 + 3(-6) + 8
y = -6(36) - 18 + 8
y = -216 - 18 + 8
y = -226
This point does not satisfy the equation.
Point (-3, -55):
y = -6(-3)^2 + 3(-3) + 8
y = -6(9) - 9 + 8
y = -54 - 9 + 8
y = -55
This point satisfies the equation.
Therefore, the correct answer is (-3, -55).