#### Answer

$y=\sqrt{4-4x^2}$

#### Work Step by Step

Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=f(cx)$ by horizontally stretching the graph of $y=f(x)$ by a factor of $c$.
Hence to horizontally stretch the graph of $y=\sqrt{4-x^2}$ by a factor of 2, we replace each occurrence of $x$ in this equation by $2x$, and, thus, obtaining the equation $$y=\sqrt{4-(2x)^2},$$ or equivalently, $$y=\sqrt{4-4x^2}.$$