To solve this for an equation that you can graph, you need to isolate the y variable. In order to do this, follow the order of operations for solving equation to get the equation.
2y^2 = x + 4 ----> divide both sides by 2
y^2 = [tex] \frac{x + 4}{2} [/tex] ----> take the square root of both sides
y = [tex] \sqrt{\frac{x+ 4}{2}} [/tex]
Now you have the equation solved for the y variable and can graph it.
