Quadratic Functions in Factored Form: Slider-Controlled Parabola
Loading the math board and drawing, please wait…
This GeoGebra applet demonstrates the graph of quadratic functions in factored form y=a(x-X_1)(x-X_2). Key mathematical concepts include: factored form of quadratic functions, parabola opening direction and width (parameter a), relationship between roots and axis of symmetry (parameters X_1 and X_2). Construction: Using slider objects a, b, c for parameters, defining function f(x)=a*(x-X_1)*(x-X_2), plotting parabola with vertex V and Y-intercept, displaying function equation via text. Suitable for middle to high school mathematics, ideal for teaching quadratic function properties and exploring relationships between roots and coefficients.
GeoGebra Commands & Parameters
Numeric N(2.5)Numeric a(0.5)Numeric M(-1.0)Point A(-3.0, -1.0)f(x) = ((a * (x - M)) * (x - N))(M, 0)(N, 0)(0, ((a * M) * N))((M + N) / 2, f((M + N) / 2))((-a) * (M + N))((a * M) * N)
AI Drawing Prompt Reference
Draw a parabola opening upwards with vertex at (-3, -1), x-intercepts at (-1, 0) and (2.5, 0), and y-intercept at (0, -1.5). Use a slider to adjust the width and direction of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.