What type of function is represented by the equation y = x^2?

The equation ( y = x^2 ) is classified as a quadratic function. Quadratic functions are polynomial functions of degree two, characterized by their standard form, which typically looks like ( y = ax^2 + bx + c ), where ( a, b, ) and ( c ) are constants and ( a \neq 0 ). In this case, the equation has the form where ( a = 1 ), ( b = 0 ), and ( c = 0 ).

Quadratic functions are known for their parabolic graphs, which open upwards or downwards depending on the sign of the leading coefficient ( a ). Since ( a ) is positive in ( y = x^2 ), the parabola opens upwards. The vertex of the parabola is located at the origin (0,0), which is the minimum point of this function.

Understanding the nature of a quadratic function allows us to differentiate it from other types of functions. Linear functions represent straight lines and have the form ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Cubic functions involve terms to the third degree, typically in the form (