Question

find out this:f is a quadratic function whose graph is a parabola opening upward and has a vertex on the x-axis. The graph of the new function g defined by g(x) = 2 - f(x - 5) has a range defined by the interval

A. [ -5 , + infinity)
B. [ 2 , + infinity)
C. ( - infinity , 2]
D. ( - infinity , 0]

Answer 1

f(x) = a(x-h)^2

f(x-5) = a(x-h-5)^2

g(x) = 2-a(x-h-5)^2
g is a parabola which opens down and has bee shifted 2 units up
range is (-inf, 2]