To determine which of the given points lies on the parabola represented by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the \( x \) values from each option into the equation and see if the resulting \( y \) value matches the \( y \) value in the point.
-
Option A: (-6, 206) \[ y = -6(-6)^2 + 3(-6) + 8 \] \[ y = -6(36) - 18 + 8 \] \[ y = -216 - 18 + 8 = -226 \quad (not\ a\ match) \]
-
Option B: (-3, 323) \[ y = -6(-3)^2 + 3(-3) + 8 \] \[ y = -6(9) - 9 + 8 \] \[ y = -54 - 9 + 8 = -55 \quad (not\ a\ match) \]
-
Option C: (-6, 8) \[ y = -6(-6)^2 + 3(-6) + 8 \] \[ y = -6(36) - 18 + 8 \] \[ y = -216 - 18 + 8 = -226 \quad (not\ a\ match) \]
-
Option D: (-3, 55) \[ y = -6(-3)^2 + 3(-3) + 8 \] \[ y = -6(9) - 9 + 8 \] \[ y = -54 - 9 + 8 = -55 \quad (not\ a\ match) \]
None of the options given seem to lie on the parabola described by the equation \( y = -6x^2 + 3x + 8 \).
It appears that there may have been an error in transcribing the problem or the options provided do not match any point on the parabola. To confirm, you could choose any \( x \) value, such as \( x = 0 \) or \( x = 1 \), compute \( y \), and see if that fits any of your options.
Let’s compute for \( x = 0 \): \[ y = -6(0)^2 + 3(0) + 8 = 8 \] Not in answer choices.
Try \( x = 1 \): \[ y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \] Not in answer choices.
If you’re looking for points on the graph that you could generate yourself, you might need to find specific \( x \) values from the quadratic equation itself.
1 answer