Thomas' Calculus 13th Edition

$y=\dfrac{1}{4}x^2-1$
Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=f\left(\dfrac{1}{c}x\right)$ by horizontally compressing the graph of $y=f(x)$ by a factor of $c$. Hence, to horizontally compress the graph of $y=x^2-1$ by a factor of 2, we replace each occurrence of $x$ in $y=x^2-1$ by $\dfrac{1}{2}x$, obtaining the equation: $$y=\left(\dfrac{1}{2}x\right)^2-1,$$$$y=\dfrac{1}{4}x^2-1.$$