Plotting and Vertical Translation of Quadratic Functions

This applet demonstrates the point-plotting method for quadratic functions and their vertical translation. It provides an interactive platform where students can plot points, graph quadratic functions, and explore how changing the parameters in the function's equation affects the position of its parabola on the coordinate plane. Through input boxes, users can adjust the coefficients and constants of quadratic functions such as y = ax² + bx + c or the vertex form y = a(x - h)² + k. By modifying these parameters, learners can directly observe how the graph shifts up or down without changing its shape or axis of symmetry. This hands-on interaction reinforces the connection between the algebraic representation of a function and its geometric visualization. The applet combines the traditional point-plotting technique with dynamic geometric transformation, offering a dual perspective that deepens conceptual understanding. Students first learn to select x-values, compute corresponding y-values, and plot the resulting points to sketch the parabola. They then explore vertical translations by varying the constant term, noting that adding a positive value to the function shifts the entire graph upward, while subtracting a value shifts it downward. The vertex moves correspondingly, while the开口方向和宽度 remain unchanged. This applet is well suited for middle school and high school mathematics instruction on quadratic functions. It supports exploration of key properties such as the vertex, axis of symmetry, maximum and minimum values, and the effect of parameter changes on the graph. Teachers can use it as a classroom demonstration tool or assign it for independent student investigation, helping learners build intuition before formal proofs or algebraic manipulations. The immediate visual feedback fosters active engagement and encourages students to formulate and test conjectures about quadratic function behavior.