Vertex is the max point, if another point is lower.
It's a downward opening parabola.
General form of the equation would be y-k=a(x-h)2 with (h,k) as the vertex
which is (1,3) h=1, k=3. All we need now is a, which we can find
using that other point (-2,-6)
The equation is y-3=a(x-1)2 now substitute x=-2 and y=-6 into that equation to solve for a
Give me another day to rethink this through. This is my first reaction, within minutes.
so final equation is y-3=-(x-1)2
That becomes y=x2-2x+4
maybe, if I haven't made a mistake somewhere, it's always possible.
check with other answers. Mistakes are very common. Some instructors
do it right in class. But it's not their lack of talent, often more than overconfidence
due to their very real talent. Maybe.