Answer
$y={4}x^2-1$
Work Step by Step
Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=f\left({c}x\right)$ 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 ${2}x$, obtaining the equation: $$y=\left({2}x\right)^2-1,$$$$y={4}x^2-1.$$
