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Product of Linear Functions

Product of Linear Functions
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2017-08-30 05:23
FunctionCoordinate GeometryOptimization
This example demonstrates how the product of linear functions affects the direction of a parabola. Key mathematical concepts include the relationship between linear functions and parabolas. By adjusting the slope and intercept of linear functions, observe changes in the parabola's direction. GeoGebra commands used include m1, m2, b2, b1, f, g, text1, text2, h, button1, var1. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Numeric m1(1.0)
  2. Numeric m2(1.0)
  3. Numeric b2(-1.0)
  4. Numeric b1(1.0)
  5. f(x) = (m1 * x) + b1
  6. g(x) = (m2 * x) + b2
  7. h(x) = (f(x) * g(x))
  8. Numeric var1(0.0)

AI Drawing Prompt Reference

Draw two lines y = 1.0*x + 1.0 and y = 1.0*x - 1.0, then calculate their product to get a parabola y = (1.0*x + 1.0)*(1.0*x - 1.0). Observe how the direction of the parabola changes.
The prompt above was compiled from the original drawing commands and is for reference only.