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Quadratic Function and Linear Equation Intersection Demo

Quadratic Function and Linear Equation Intersection Demo
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2016-02-16 08:53
VectorFunctionCoordinate GeometryGraphing
This example demonstrates the process of finding the intersection points between a quadratic function and a linear equation. Core math concepts include quadratic functions, linear equations, analytical geometry, and vector operations. It utilizes commands like Cartesian Curve and Surface, along with objects such as a, b, rot, c, p, q, ns, r, nl, nt, o, l, m, n, h, g, e, f, i, j, k, d for construction. Suitable for high school mathematics education, illustrating function intersections, vector operations, and the application of parametric equations.

GeoGebra Commands & Parameters

  1. CurveCartesian((b * tan(t / 2)), ((a * sin((nt * t))) * cos(rot)) - ((sin(rot) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(rot)) + ((cos(rot) * a) * (cos((nt * t)) + 1)), t, 0, (2 * π)) → o
  2. Surface((b * tan(t / 2)), ((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), t, -3.14159, π, v, 0, (2 * π / 3)) → l
  3. Surface((b * tan(t / 2)), ((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), t, -3.14159, π, v, (2 * π / 3), (4 * π / 3)) → m
  4. Surface((b * tan(t / 2)), ((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), t, -3.14159, π, v, (4 * π / 3), (2 * π)) → n
  5. CurveCartesian(((a * sin((nt * t))) * cos(rot)) - ((sin(rot) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(rot)) + ((cos(rot) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), t, -3.14159, π) → h
  6. CurveCartesian(((a * sin((nt * t))) * cos(rot)) - ((sin(rot) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), ((a * sin((nt * t))) * sin(rot)) + ((cos(rot) * a) * (cos((nt * t)) + 1)), t, -3.14159, π) → g
  7. Surface(((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), t, -3.14159, π, v, (2 * π / 3), (4 * π / 3)) → e
  8. Surface(((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), t, -3.14159, π, v, (4 * π / 3), (2 * π)) → f
  9. Surface(((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), t, -3.14159, π, v, 0, (2 * π / 3)) → i
  10. Surface(((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), t, -3.14159, π, v, (2 * π / 3), (4 * π / 3)) → j
  11. Surface(((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), t, -3.14159, π, v, (4 * π / 3), (2 * π)) → k
  12. Surface(((a * sin((nt * t))) * cos(v)) - ((sin(v) * a) * (cos((nt * t)) + 1)), ((a * sin((nt * t))) * sin(v)) + ((cos(v) * a) * (cos((nt * t)) + 1)), (b * tan(t / 2)), t, -3.14159, π, v, 0, (2 * π / 3)) → d