Question

Which of the following statement describes the graph of the parabola with the equation f(x)=-3x2.

A. The parabola opens down, goes through (-2, 0), has a vertex at (-0.5, 6.75), and goes through (1, 0).

B. The parabola opens up, goes through (-2, 0), has a vertex at (-0.5, 6.75), and goes through (1, 0).

C. The parabola opens down, goes through (-2, 0), has a vertex at (-0.5, -6.75), and goes through (1, 0).

Answer 1

The equation f(x) = -3x^2 describes a parabola that opens downward with its vertex at the origin. All given options A, B, and C are incorrect in their descriptions of this specific parabola's graph.

Step-by-step explanation:

The correct description of the graph of the parabola with the equation f(x) = -3x2 is that the parabola opens downward. This is because the coefficient of the x2 term is negative. As for the specifics of the parabola's behavior, since there are no x or constant terms and the parabola is in standard form, the vertex would be at the origin, which is (0, 0), not (-0.5, 6.75), as option A suggests. Also, the parabola would not pass through (-2, 0) or (1, 0) because when x is either -2 or 1, the value of f(x) would not be zero; rather, it would be positive since we would be squaring a negative number and multiplying by a negative constant. Therefore, all listed options A, B, and C are incorrect regarding this parabola's graph.