Answer:
y + 2 = -2(x - 3)^2
Step-by-step explanation:
We can see immediately that the vertex is at (3, -2).
The vertex form of the equation of a parabola is
y - k = a(x - h)^2.
If the parabola opened upward, the equation would be y + 2 = 2(x - 3)^2. But seeing that this particular parabola opens downward, the equation is
y + 2 = -2(x - 3)^2.
Check: Does the point (2, -4) satisfy this equation?
-4 + 2 = -2(2 - 3)^2 becomes -2 = -2(-1)^2, which is true.
