Chapter 4 - Quadratic Functions - 4.4 Solving Quadratic Equations by the Square Root Property and Completing the Square - 4.4 Exercises - Page 349: 65

$g(x) =0.5\left(x+7\right)^2-54.5$

The conversion of the function to the standard vertex form is self explanatory. All mathematical steps are shown below. $$ \begin{aligned} g(x)&=0.5 x^2+7 x-30\\ & = 0.5\left( x^2+\frac{7}{0.5} x\right) -30\\ &= 0.5\left( x^2+14x\right) -30\\ & = 0.5\left(x^2+14x+ 7^2 \right)-30-0.5\cdot 7^2 \\ & =0.5\left(x+7\right)^2-54.5\\ \end{aligned} $$