Set 17: Quadratic Equations (Intermediate)

Choice A is correct. Choice A is the correct answer. The direction a parabola opens is determined by the leading coefficient $a$. 1. Here, $f(x) = -1 x^2 + 6 x$, so $a = -1$. 2. Since $a < 0$, the parabola opens downward (like a frown). 3. Therefore, the vertex is the highest point on the graph, representing a Maximum. Choice B is incorrect because a minimum occurs when $a > 0$ (opens upward). Choice C is incorrect because a parabola cannot have both. Choice D is incorrect because every parabola has a vertex that is either a max or min.