For h(x), to find out the maximum, you would need to use this formula:

We are given the equation:
.
So, a = -1, b = 4, and c = -2. Then, substitute the numbers into the formula:
h(x)'s maximum =

=

=

=

=

For g(x), to find out the maximum, just look at the highest point of y on the graph of the function, which is 2.
Thus, the answer you have chosen is the correct answer, which is choice 3: functions g and h have the same maximum of 2. Hope this helps :)