To determine which point can be generated from the quadratic equation \( y = -6x^2 + 3x + 8 \), we need to compute the value of \( y \) for various values of \( x \).
First, let's express the equation clearly:
\[ y = -6x^2 + 3x + 8 \]
Now, we can evaluate \( y \) for \( x = -6 \) and \( x = -3 \).
- For \( x = -6 \):
\[ y = -6(-6)^2 + 3(-6) + 8 \] \[ = -6(36) - 18 + 8 \] \[ = -216 - 18 + 8 \] \[ = -216 - 10 \] \[ = -226 \]
So, the point for \( x = -6 \) is \( (-6, -226) \), which does not match either of the choices.
- For \( x = -3 \):
\[ y = -6(-3)^2 + 3(-3) + 8 \] \[ = -6(9) - 9 + 8 \] \[ = -54 - 9 + 8 \] \[ = -54 - 1 \] \[ = -55 \]
So, the point for \( x = -3 \) is \( (-3, -55) \), which matches one of the given choices.
Thus, the correct answer is:
(-3, -55)
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