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Quadratic Equations In 2 Variables

Quadratic Equations In 2 Variables
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2018-08-22 22:31
FunctionCoordinate GeometryGeometric Construction
In collections Conics
This example demonstrates how to construct and visualize quadratic equations in two variables using geometric methods and graphing. Key mathematical concepts include quadratic functions, coordinate geometry, and geometric construction. The construction involves GeoGebra commands such as Vector, Point, Segment, Rotate, Angle, Translate, Center, and CircleArc. Suitable for middle or high school mathematics to understand the properties of quadratic functions and their graphical representation.

GeoGebra Commands & Parameters

  1. Vector(H_1, E_1) → w_1
  2. Vector(I_1, J_1) → a_1
  3. Point(w_1) → B_1
  4. Segment(O_1, G_1) → h_1
  5. Rotate(G_1, 30°, O_1) → K_1
  6. Segment(O_1, K_1) → i_1
  7. Angle(G_1, O_1, K_1) → δ_1
  8. Segment(G_1, L_1) → k_1
  9. Segment(K_1, N_1) → l_1
  10. Segment(K_1, P_1) → m_1
  11. Segment(G_1, M_1) → n_1
  12. Segment(O_1, K_1) → f
  13. Segment(N_1, K_1) → g
  14. Translate(c661, Vector[(s662 * Vector[(sqrt(2) / 2, (5 * sqrt(2) / 2))])]) → c662
  15. Rotate(c662, (((-s663) * 45))°, O66) → c663
  16. Center(c662) → A
  17. Center(c663) → B
  18. Vector(O66, A) → u
  19. CircleArc(O66, B, A) → c
  20. Angle(L_1, O_1, G_1) → α
  21. Angle(G_1, O_1, K_1) → β

AI Drawing Prompt Reference

Start by placing a point G at the origin O and drawing the segment OG. Rotate G around O by 30 degrees to obtain point K, then draw segment OK and mark the angle δ between G, O, and K. From G draw a segment to point L, and from K draw segments to points N, P, and M. Apply a translation and a rotation to create two circles, find their centers A and B, and draw a vector from O66 to A. Using O66, B, and A, construct a circular arc c. Finally, label the angles α (between L, O, G) and β (between G, O, K) to complete the geometric construction of a quadratic equation in two variables.
The prompt above was compiled from the original drawing commands and is for reference only.