For the graph of

to have a maximum value, it must open downward which means that its leading
coefficient, a, must be negative.

y is its maximum value at the vertex when x=1, so we substitute 1 for x and 2
for y






The formula for the x coordinate of the vertex is:


So




Substitute -1 for a in





To check, substitute -1 for a and 1 for c in





Then graph:

 

Edwin