The equation y = x^2 represents a quadratic function, where y is the output and x is the input. This function produces a parabolic graph that opens upwards. For every value of x , y is equal to x multiplied by itself. For example, if x = 2 , then y = 2^2 = 4 . The graph of y = x^2 has its vertex at the point 0, 0, which is the lowest point on the curve. As x moves away from zero in either direction, y increases rapidly. This function is commonly studied in algebra and has applications in various fields, including physics and engineering.