It is not, because the definition of a function includes the requirement that no x will have more than one corresponding y. The parabola you named has its vertex at (0,0) and opens to the right, so every x value > 0 will have two corresponding y values, one positive and one negative. For example, if x = 4, y = 2 and -2. Remember the vertical line test; if you can draw a vertical line anywhere that crosses more than one point on the graph, it is not a function.
