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Find Zeros, Intercepts, Vertex, and Axis of Symmetry of a Quadratic Function

Find Zeros, Intercepts, Vertex, and Axis of Symmetry of a Quadratic Function
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2014-09-12 03:19
FunctionCoordinate GeometrySlider AnimationLocusGraphing
In collections CCGPS AA Unit 6 Lesson 1
This example demonstrates how to find the zeros, intercepts, vertex, and axis of symmetry of the quadratic function f(x) = 3x^2 – 2x – 5. Key mathematical concepts include the properties of quadratic functions, the vertex formula, and the axis of symmetry. GeoGebra commands used include If, Simplify, GCD, FractionText, Corner, Polygon, etc. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. If(u ≟ 1, 2, If[GCD[u, v] ≟ 1, u, u + 1]) → a
  2. If(GCD[a, v] ≟ 1, v, v + 1) → v1
  3. Simplify(ffact) → f
  4. GCD(u, v) → test
  5. FractionText(yvert) → yverttext
  6. Corner(3) → C3
  7. Corner(1) → C1
  8. Corner(4) → C4
  9. Corner(2) → C2
  10. Polygon(C2, C3, (Edge, y(C3)), (Edge, y(C2))) → Mask, c2, c3, d, e
  11. FractionText(Vx) → xverttext

AI Drawing Prompt Reference

Draw the quadratic function f(x) = 3x^2 - 2x - 5, and find its zeros, intercepts, vertex, and axis of symmetry. First, plot the function, then determine the vertex coordinates, calculate the axis equation, find the x-intercept and y-intercept, and finally mark the vertex and axis.
The prompt above was compiled from the original drawing commands and is for reference only.