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Quadratic Inequalities Solver: Graph & Solution Set for ax²+bx+c≷0

Quadratic Inequalities Solver: Graph & Solution Set for ax²+bx+c≷0
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2015-12-15 21:33
FunctionCoordinate GeometryInequalityGraphing
In collections Kvadratna funkcija - Quadratic function
① This example demonstrates the graph of the quadratic function f(x)=ax²+bx+c and the corresponding solution intervals of the inequality ax²+bx+c≷0 on the number line. ② Core mathematical concepts include quadratic function graphs, discriminant analysis, root locations, and case‑by‑case inequality solving (parabola opening up/down, Δ>0, =0, <0). ③ Construction highlights: Intersect command finds x‑intercepts X₁, X₂; Textfield and inputBoxa/b/c create adjustable parameters a, b, c; object f defines the quadratic; auxiliary objects d, n1, n2, X12 mark key coordinates; dynamic text objects (textxizR, textmanje, etc.) display solution intervals in real time. ④ Suitable for high‑school algebra (compulsory modules) and college‑prep review, ideal for teacher demonstrations and student self‑exploration.

GeoGebra Commands & Parameters

  1. Intersect(f, xAxis, 1) → X_1
  2. Intersect(f, xAxis, 2) → X_2
  3. Intersect(f, xAxis, 1) → X12
  4. Textfield(a) → inputBoxa
  5. Textfield(b) → inputBoxb
  6. Textfield(c) → inputBoxc

AI Drawing Prompt Reference

Draw the graph of a quadratic function and show its x-intercepts, while displaying the solution set of the inequality on a number line. Adjust the coefficients a, b, c via input boxes to dynamically update the function graph and x-intercepts, and show the solution intervals of the inequality on the number line in real time.
The prompt above was compiled from the original drawing commands and is for reference only.