Intersection of a Parabola and a Line by Brian Sterr

This example demonstrates how to find the intersection points between a parabola and a line in a coordinate plane, allowing dynamic observation of how the number and positions of intersections change as parameters vary. The core mathematical concepts involve solving a system of a quadratic and a linear equation, the discriminant's role in determining the number of real solutions, and coordinate geometry for locating intersection points. Construction highlights: using GeoGebra's Line command to create the line, Intersect command to compute intersection points, and sliders or text objects (such as m, c, h, k, p, text1, text2) to control parameters, generating points A, B, C, D. Suitable for middle and high school students learning the relationship between quadratic functions and lines, equation solving, and visual reasoning in algebra and geometry.