Answer:
f(x) = -(x-4)^2 + 5
Step-by-step explanation:
The function [tex]f(x) = -(x-4)^2 + 5[/tex] is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.
Proving that [tex]f(x) = -(x-4)^2 + 5 \le 5[/tex] for all x:
[tex]x^2 \ge 0 \Rightarrow (x-4)^2 \ge 0 \Rightarrow -(x-4)^2 \le 0 \Rightarrow -(x-4)^2 + 5 \le 5.[/tex]
