Graph of the Quadratic Function y = x² - a

This GeoGebra applet demonstrates the graph of the quadratic function y = x² - a and its dynamic transformations. By adjusting the parameter a, users can visually observe the vertical translation of the parabola y = x² along the y-axis. This interactive visualization helps in understanding how parameter changes affect the position of the quadratic function's graph, exploring key properties such as the vertex coordinates, the axis of symmetry, and the direction of opening. The applet provides an intuitive way for students to see that as a increases, the parabola shifts downward, and as a decreases, it shifts upward. The vertex of the parabola is located at (0, -a), and the axis of symmetry remains the y-axis regardless of the value of a. Since the coefficient of x² is positive, the parabola always opens upward. This makes the applet a practical tool for learning function graph transformations and analytic geometry, allowing students to connect algebraic expressions with their geometric representations in a dynamic and engaging manner.