Summary: {\it Y. Wang} and {\it Y.-N. Yeh} [Eur. J. Comb. 26, No. 5, 617‒627 (2005; Zbl 1076.05010)] proved that if $P(x)$ is a polynomial with nonnegative and nondecreasing coefficients, then $P(x+ d)$ is unimodal for any $d> 0$. A mode of a unimodal polynomial $f(x)= a_0+a_1 x+\cdots+ a_m x^m$ is an index $k$ such that $a_k$ is the maximum coefficient. Suppose that $M_*(P,d)$ is the smallest mode of $P(x+ d)$, and $M^*(P,d)$ the greatest mode. {\it Y. Wang} and {\it Y.-N. Yeh} [loc. cit.] conjectured that if $d_2> d_1> 0$, then $M_*(P,d_1)\ge M_*(P,d_2)$ and $M^*(P,d_1)\ge M^*(P,d_2)$. We give a proof of this conjecture.