Set 9: Quadratic Equations (Advanced)

Choice A is correct. Choice A is the correct answer. The vertex form of a quadratic equation is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. Here, the vertex (maximum point) is $(-2, 5)$, so $h = -2$ and $k = 5$. Substituting these values gives $E(x) = a(x - (-2))^2 + 5 = a(x + 2)^2 + 5$. Since the particle reaches a maximum energy, the parabola must open downward, meaning $a$ must be negative. Choice A has $a = -1$ and the correct vertex structure. Choice B is incorrect because it corresponds to a vertex at $(2, 5)$. Choice C is incorrect because it corresponds to a vertex at $(2, -5)$. Choice D is incorrect because it corresponds to a vertex at $(-2, -5)$ and opens upward (minimum).