$\displaystyle a_0= -\frac{1}{3}$, $\displaystyle a_1= \frac{1}{3}$, $\displaystyle a_2= -\frac{4}{3}$, $\displaystyle a_3= \frac{5}{3}$, and $\displaystyle a_4= -\frac{1}{3}$ again.
Taking absolute values, $\displaystyle |a_0|= \frac{1}{3}$, $\displaystyle |a_1|= \frac{1}{3}$, $\displaystyle |a_2|= \frac{4}{3}$, $\displaystyle |a_3|= \frac{5}{3}$, and $\displaystyle |a_4|= \frac{1}{3}$ so we really only have three different values, $\displaystyle \frac{1}{3}$, $\displaystyle \frac{4}{3}$, and $\displaystyle \frac{5}{3}$.
The largest (max) of those is $\displaystyle \frac{5}{3}$ so $\displaystyle 1+ max(|a_0, a_1, a_2, a_3, a_4)$ is $\displaystyle 1+ \frac{5}{3}= \frac{3}{3}+ \frac{5}{3}= \frac{8}{3}$.
The difference between the two is that in the first one, you add all the fractions, to get 4, then take the larger of 1 and 4. In the second, you take the largest of the fractions, then add 1 to that.