Question

What is the range of the graph of y = –3(x – 2)^2 + 3?

Answer 1

\[f(x) \leq 3\]
Reason? The quantity \[(x-2)^2\geq 0\]
for all \[x \in \mathbb{R}.\]
Hence \[-3(x-2)^2 \leq 0\]
Therefore \[f(x) = -3(x-2)^2 + 3 \leq 3\]

Answer 2

So a nice subsequent question is:
For what value of \[x\] does \[f(x)\] take it's largest value 3?