Question 21

The coordinates of the vertex of the parabola are (3, 3).

The vertex of the parabola represented by the equation y = -3x² + 18 - 24 can be found using the vertex formula. After simplifying the equation to y = -3x² - 6, we find that the vertex is located at the point (3, 3).

A) (6,-24)

This option is incorrect as the coordinates do not correspond to the vertex of the parabola. When the equation is analyzed, the maximum point of the parabola, which is the vertex, does not occur at (6, -24).

B) (4,0)

This choice is incorrect because the vertex does not lie at (4, 0). The vertex calculation reveals that the maximum point of the parabola is not found at this coordinate, thus it does not represent the vertex.

C) (3,3)

This option is correct as it represents the vertex of the parabola derived from the equation. The vertex of the parabola occurs at x = 3, and substituting this value back into the equation yields a y-coordinate of 3, confirming (3, 3) as the vertex.

D) (2,0)

This choice is incorrect as the coordinates (2, 0) do not represent the vertex of the parabola. Evaluating the vertex through the vertex formula shows that this point is not where the maximum value occurs.

E) (-3,-105)

This option is also incorrect because the coordinates (-3, -105) do not correspond to the vertex of the parabola. The calculations for the vertex indicate that this coordinate does not reflect the maximum point of the parabola.

Conclusion

The correct answer is definitively (3, 3) as it is derived directly from the vertex calculation of the quadratic equation. All other options fail to represent the vertex as they do not correspond to the maximum point of the parabola defined by the given equation.