Parabolas as Products of Linear Functions

This GeoGebra worksheet demonstrates that when two linear functions are multiplied to produce a quadratic function, the resulting parabola's roots are identical to the roots of the original linear functions. The example visually connects the x-intercepts of the linear functions with the zeros of the parabola, reinforcing the relationship between linear and quadratic representations. Key construction elements include the use of the Intersect command to locate roots, linear functions defined by slope and intercept parameters, and function graphs plotted on the coordinate plane. It is designed for high school algebra and functions courses, helping students grasp the geometric meaning of multiplying linear expressions to form a quadratic polynomial.