Use this interactive applet to explore the properties of quadratic functions in the general form \( f(x) = ax^2 + bx + c \), where \( a \neq 0 \). Adjust the sliders or input values for the coefficients \( a \), \( b \), and \( c \) to observe how they affect the shape, opening direction, vertex, and intercepts of the parabola in real time. The red point indicates the vertex, which represents the minimum (if \( a > 0 \)) or maximum (if \( a < 0 \)) value of the function.