Chapter 4 - Quadratic Functions - 4.4 Solving Quadratic Equations by the Square Root Property and Completing the Square - 4.4 Exercises - Page 349: 54

$ f(x) = (x-5)^2-32$

The conversion of the function to the standard vertex form is self explanatory. All mathematical steps are shown below. $$ \begin{aligned} g(x) & = x^2-10 x-7\\ & = x^2-10 x+\left(\frac{10}{2}\right)^2 -7-\left(\frac{10}{2}\right)^2 \\ & =\left(x^2-10 x+5^2\right)-7-5^2 \\ & =(x-5)^2-32. \end{aligned} $$