To find a point that lies on the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the values of \( x \) from each of the provided point options into the equation and see if we get the corresponding \( y \) value.
Let's calculate \( y \) for each of the given points:
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For the point \( (-6, 206) \): \[ y = -6(-6)^2 + 3(-6) + 8 \] \[ = -6(36) - 18 + 8 \] \[ = -216 - 18 + 8 \] \[ = -226 \quad \text{(not 206)} \]
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For the point \( (-6, 8) \): \[ y = -6(-6)^2 + 3(-6) + 8 \] The calculation is the same as above and results in \( y = -226 \quad \text{(not 8)} \).
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For the point \( (-3, -55) \): \[ y = -6(-3)^2 + 3(-3) + 8 \] \[ = -6(9) - 9 + 8 \] \[ = -54 - 9 + 8 \] \[ = -55 \quad \text{(this is correct)} \]
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For the point \( (-3, 323) \): \[ y = -6(-3)^2 + 3(-3) + 8 \] The calculation is the same as above and results in \( y = -55 \quad \text{(not 323)} \).
The only point that lies on the parabola given by the quadratic equation \( y = -6x^2 + 3x + 8 \) is:
Answer: \((-3, -55)\)