Answer
Horizontal shift, vertical shrink, reflection, horizontal shift (see graph)
Work Step by Step
We are given the function:
$N(x)=-0.023(x-33.12)^2+131$, $0\leq t\leq 14$
Describe the transformation of the parent function $f(x)=x^2$.
Horizontally shift $f(x)$ 33.12 units to the right to get $a(x)=(x-33.12)^2$.
Vertically shrink $a(x)$ by a factor of 0.023 to get $b(x)=0.023(x-33.12)^2$.
Reflect $b(x)$ across the $x$-axis to get $c(x)=-0.023(x-33.12)^2$.
Vertically shift $c(x)$ 131 units upward to get $N(x)=-0.023(x-33.12)^2+131$.
Graph $N(x)$.
