Answer
The Bézier curve is
$c(t)=(3-9 t+24 t^2-16 t^3,2+6 t^2-4 t^3)$ for $0\leq t \leq 1$.
Work Step by Step
Since
$P_0=\left(a_0,b_0\right)=(3,2)$,
$P_1=\left(a_1,b_1\right)=(0,2)$,
$P_2=\left(a_2,b_2\right)=(5,4)$,
$P_3=\left(a_3,b_3\right)=(2,4)$.
Substituting these values into Eq. (9) and Eq. (10) we obtain the parametric equations
$x(t)=3-9 t+24 t^2-16 t^3$,
$y(t)=2+6 t^2-4 t^3$.
Thus, $c(t)=(3-9 t+24 t^2-16 t^3,2+6 t^2-4 t^3)$ for $0\leq t \leq 1$.
