Answer
$y=\sqrt{4-\dfrac{1}4x^2}$
Work Step by Step
Given the graph of $y=f(x)$ and a real number $c>1$, we obtain the graph of $y=f(\dfrac{x}{c})$ 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 $x/2$, and, thus, obtaining the equation $$y=\sqrt{4-(\dfrac{x}{2})^2},$$ or equivalently, $$y=\sqrt{4-\dfrac{x^2}{4}}.$$
