Y^2+2=x is not a function in terms of x, but y=√x is a function. The 4th quadrant is still positive for x so those values are still valid values. So my points would be (66,8), (66,-8), (102,10), (102,-10), (123,11), (123,-11) as an example.

A function is a relation that is one to one. Such that if f(x)=y then for every x there is exactly one y value. When graphed you can use ther vertical line test. If the line passes through 2 or more points on the graph at any location then it is not a function.

Question to you then: What makes y=√(x-2) the answer over y=-√(x-2)?

Remember that when you take the square root of both sides you get + and - the square root.... So you have 2 functions y=√(x-2) and y=-√(x-2). So to plot the equation y^2+2=x you'll have to plot both those equations above.