Product of Linear Functions: Exploring Parabola Opening Direction

This GeoGebra example dynamically demonstrates how the product of two linear functions forms a quadratic function (parabola), and how adjusting the linear parameters changes the parabola's opening direction and shape. Core mathematical concepts include linear functions, quadratic functions, function multiplication, parabola concavity, zeros, axis of symmetry, and the relationship between the linear factors and the resulting curve. The construction uses sliders (var1) to control parameters, defines linear functions f and g with slopes (m1, m2) and intercepts (b1, b2), creates the product function h, and includes text objects (text1, text2) and a button (button1) for interactive exploration. Suitable for middle and high school students learning function transformations, quadratic properties, and dynamic geometry, this example helps visualize how linear factor products determine the parabola's opening direction and its intersections with the x-axis.