Answer
Start with $g(x)=x^{2}$,
Reflect abouth the x-axis, $\quad-g(x)=-x^{2}$
Compress vertically by factor $\displaystyle \frac{1}{4},\displaystyle \qquad-\frac{1}{4}g(x)=-\frac{1}{4}x^{2}$
Work Step by Step
Start with $g(x)=x^{2}$,
Reflect abouth the x-axis, $\quad-g(x)=-x^{2}$
Compress vertically by factor $\displaystyle \frac{1}{4},\displaystyle \qquad-\frac{1}{4}g(x)=-\frac{1}{4}x^{2}$