`y=-(x-3)^2+a`
In the equation above, a is a constant. The graph of the equation in the xy-plane is a parabola. Which of the following is true about the parabola?

Options

A. Its minimum occurs at (−3, a).
B. Its minimum occurs at (3, a).
C. Its maximum occurs at (−3, a).
D. Its maximum occurs at (3, a).

Answer

D

Explanation

The vertex form of a quadratic equation is`y = n(x − h)^2 + k`, where (h, k) gives the coordinates of the vertex of the parabola in the xy-plane and the sign of the constant n determines whether the parabola opens upward or downward. If n is negative, the parabola opens downward and the vertex is the maximum. The given equation has the values h = 3, k = a, and n = −1. Therefore, the vertex of the parabola is (3, a) and the parabola opens downward. Thus, the parabola’s maximum occurs at (3, a)
Choice A is incorrect and may result from interpreting the given equation as representing a parabola in which the vertex is a minimum, not a maximum, and from misidentifying the value of h in the given equation as −3, not 3. Choice B is incorrect and may result from interpreting the given equation as representing a parabola in which the vertex is a minimum, not a maximum. Choice C is incorrect and may result from misidentifying the value of h in the given equation as not 3.