If g(x)=x+3 h(x)=9-x^2, what is the maximum of h(g(x))?

Answer 1

h(g(x)) = 9 - (x + 3)^2
... = -x^2 - 6x

the max is on the axis of symmetry
... x = -b / 2a = 6 / -2 = -3

plug in -3 to find the maximum