In the standard form of a parabola, what does the parameter 'c' represent?

In the standard form of a parabola, represented as ( y = ax^2 + bx + c ), the parameter 'c' specifically denotes the y-intercept of the graph. This means that when ( x = 0 ), the value of the parabola can be determined directly from 'c', as substituting 0 for x gives the equation ( y = c ). Thus, the point where the parabola crosses the y-axis is given by the coordinates ( (0, c) ).

Identifying 'c' as the y-intercept is important for graphing the parabola, as it provides a key starting point. Additionally, understanding this can help in analyzing the behavior of the parabola and its symmetry about its axis of symmetry. The correct identification of 'c' is fundamental in illustrating the characteristics of the parabola on a coordinate plane.