Work Step by Step
We are given the function: $f(x)=3(x-2)^2+1$ We start graphing with the basic function $a(x)=x^2$. We horizontally shift $a(x)$ by 2 units to the right to get $b(x)=(x-2)^2$. Then we vertically stretch $b(x)$ by a factor of 3 to get $c(x)=3(x-2)^2$. Finally we vertically shift $c(x)$ one unit upward to get $f(x)=3(x-2)^2+1$. We use 3 points: $(1,4),(2,1),(3,4)$.