Answer
$y=-3\ cos(\frac{1}{2}x)$
Work Step by Step
Step 1. As the curve is even and passes $(0,-3)$, we can write a general form $y=-A\ cos(kx)$
Step 2. We can identify the amplitude $A=3$.
Step 3. We can identify the period $p=4\pi$,thus $\frac{2\pi}{k}=4\pi$ and $k=\frac{1}{2}$
Step 4. The equation is $y=-3\ cos(\frac{1}{2}x)$
