Answer
$y=-\frac{5}{2}\ cos(\pi x)$
Work Step by Step
Step 1. As the curve is even and passes $(0,-\frac{5}{2})$, we can write a general form $y=-A\ cos(kx)$
Step 2. We can identify the amplitude $A=\frac{5}{2}$.
Step 3. We can identify the period $p=2$, thus $\frac{2\pi}{k}=2$ and $k=\pi$
Step 4. The equation is $y=-\frac{5}{2}\ cos(\pi x)$
