Exploring Quadratic Functions: Standard Form
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This example demonstrates how students can use sliders to adjust the three coefficients in the standard form of a quadratic function's equation, observing the changes in the parabola's shape. Key math concepts include quadratic functions, standard form, coefficient effects, and parabola characteristics. It utilizes GeoGebra commands/objects like c, a, b, f, V, Y, X1, X2, A, Formula. Suitable for high school mathematics education to understand the relationship between the function's graph and its coefficients, and the impact of parameter changes on the function's shape.
GeoGebra Commands & Parameters
Numeric c(0.0)Numeric a(1.0)Numeric b(0.0)f(x) = (a * x^(2)) + (b * x) + c(((-b)) / ((2 * a)), f(((-b)) / ((2 * a))))(0, c)(((-b)) / ((2 * a)) - sqrt(b^(2) - ((4 * a) * c)) / ((2 * a)), 0)(((-b)) / ((2 * a)) + sqrt(b^(2) - ((4 * a) * c)) / ((2 * a)), 0)Point A(-3.0, -1.0)