To determine which point is on the parabola described by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can substitute the x-coordinates from the options into the equation and see if the corresponding y-value matches.
Let's evaluate each option:
-
For option A: \( (-3, -55) \) \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \] This point is on the parabola.
-
For option B: \( (-6, 8) \) \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] This point is not on the parabola.
-
For option C: \( (-3, 323) \) \[ y = -6(-3)^2 + 3(-3) + 8 = -6(9) - 9 + 8 = -54 - 9 + 8 = -55 \] This point is not on the parabola.
-
For option D: \( (-6, 206) \) \[ y = -6(-6)^2 + 3(-6) + 8 = -6(36) - 18 + 8 = -216 - 18 + 8 = -226 \] This point is not on the parabola.
From the evaluations, the only point that lies on the parabola for the equation \( y = -6x^2 + 3x + 8 \) is:
A. (-3, -55).
1 answer