Exploring Parabolas by wtruong

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2013-05-07 03:01

In collections Quadratics - Parabolas

This example demonstrates the geometric properties of parabolas and how changes in parameters affect the graph. Core math concepts include function graphing, coordinate geometry, parameter control, and geometric transformations. GeoGebra commands and objects used are: a, h, k, f, c, text1, text2, b, d, pic1, e, A, B, pic2, g, C, D, pic3, i, E, F, pic4, j, G, H, pic5, l, I, J, pic6, m, K, L, pic7, n, M, N, pic8, o, O. Suitable for high school mathematics teaching or student self-exploration of function properties.

GeoGebra Commands & Parameters

Numeric a(0.0)
Numeric h(0.1)
Numeric k(0.0)
f(x) = a * (x - h)^(2) + k
y = a * (x - h)^(2) + k
Boolean b(true)
Boolean d(true)
Boolean e(false)
Point A(0.0, 0.0)
Point B(28.187952150746906, 0.0)
Boolean g(false)
Point C(0.07216481248967366, -0.018031918839640504)
Point D(28.260116963236584, -0.018031918839640504)
Boolean i(false)
Point E(0.07216481248967455, -0.018031918839640504)
Point F(28.26011696323658, -0.018031918839640504)
Boolean j(false)
Point G(0.11620848772521697, -0.018031918839639616)
Point H(28.30416063847212, -0.018031918839639616)
Boolean l(false)
Point I(-0.10400988845249515, -0.15016294454626777)
Point J(28.08394226229441, -0.15016294454626777)
Boolean m(false)
Point K(0.028121137254132123, -0.15016294454626777)
Point L(28.21607328800104, -0.15016294454626777)
Boolean n(false)
Point M(0.0, 0.0)
Point N(18.0, 0.0)
Boolean o(false)
Point O(0.028121137254132123, 0.026011756395900143)
Point P(28.216073288001038, 0.026011756395900143)
Boolean p(false)

AI Drawing Prompt Reference

Draw a parabola with vertex at (h, k), where a, h, and k are adjustable parameters. Start by setting a to 0.0, h to 0.1, and k to 0.0, then plot the parabola y = a * (x - h)² + k. Adjust the values of a, h, and k to observe how the parabola changes.

The prompt above was compiled from the original drawing commands and is for reference only.