Chapter 4 - Quadratic Functions - 4.4 Solving Quadratic Equations by the Square Root Property and Completing the Square - 4.4 Exercises - Page 349: 62

$k(p) =5(p-5)^2-105$

The conversion of the function to the standard vertex form is self explanatory. All mathematical steps are shown below. \begin{aligned} k(p)&=5 p^2-50 p+20\\ & = 5\left(p^2-10 p\right) +20 \\ & = 5\left[p^2-10 p+\left( \frac{10}{2} \right)^2 \right]+20-5\cdot \left( \frac{10}{2} \right)^2 \\ & =5(p^2-10 p+5^2)^2+20-5\cdot 5^2\\ &= 5(p-5)^2-105. \end{aligned}