Parabolas through two points
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This example demonstrates that an infinite number of parabolas can pass through any two given points, which are functions if the x-coordinates are distinct. It involves core concepts like parabola equations, coordinate geometry, and parametric equations. The construction uses GeoGebra objects A (point), B (point), t (slider), and f (function). Suitable for high school and above students to understand function graphs and parametric equations.
GeoGebra Commands & Parameters
Point A(2.0, 3.0)Point B(5.0, -1.0)Numeric t(-2.2)f(x) = (((1 / 10 * t) - 17 / 30) * x^(2)) + (((((-7)) / 10 * t) + 79 / 30) * x) + t
AI Drawing Prompt Reference
Draw parabolas passing through two points A(2,3) and B(5,-1). By adjusting the value of parameter t, you will see an infinite number of parabolas passing through these two points. First, create points A and B, then use parameter t to construct the parabola equation and observe how the parabola changes as t varies.
The prompt above was compiled from the original drawing commands and is for reference only.