Answer
$m(p) =6\left(p+\frac{5}{6}\right)^2+\frac{101}{6}$
Work Step by Step
The conversion of the function to the standard vertex form is self explanatory. All mathematical steps are shown below. $$
\begin{aligned}
m(p)&=6 p^2+10 p+21\\
& = 6\left( p^2+\frac{10}{6} p\right) +21\\
&= 6\left( p^2+\frac{5}{3} p\right) +21\\
& = 6\left[p^2+\frac{5}{3} p+\left( \frac{5}{6} \right)^2 \right]+21-6\cdot \left( \frac{5}{6} \right)^2 \\
& =6\left(p+\frac{5}{6}\right)^2+\frac{21\cdot 6}{6}- \frac{25}{6}\\
&= 6\left(p+\frac{5}{6}\right)^2+\frac{101}{6}.
\end{aligned}
$$
