To determine a point on the parabola represented by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can plug in the x-coordinates from the answer choices into the equation and see which generates a corresponding y-coordinate.
Let's evaluate each x-coordinate given in the response options:
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For \( x = -6 \): \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \quad \text{(not } (−6,8) \text{)} \]
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For \( x = -3 \): \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \quad \text{(this is } (−3,−55) \text{)} \]
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For \( x = -3 \) again (to confirm): \[ y = -6(-3)^2 + 3(-3) + 8 = -54 - 9 + 8 = -55 \quad \text{(still } (−3,−55) \text{)} \]
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For \( x = -6 \) again (confirming): \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -226 \quad \text{(not } (−6,206) \text{)} \]
So, when plugging in the x-coordinates from the options, we find that:
The correct point generated from the quadratic equation is \( (-3, -55) \).
The answer is: (−3,−55)