AlgebraExplorer

Some to try...

Cube root of 8
- GeoGebra: nroot(8,3):
- Enter \nthroot3[space]8[space]
Greatest Common Divisor of 24 and 32
- GeoGebra: GCD(24,32):
- Enter gcd(24,32)
Continued Fraction for \(\sqrt{m}\)
- GeoGebra: ContinuedFraction(\(\sqrt{m}\)):
- Enter cf(\sqrt(m[space])

Define and plot \(ax^n+bx+c\)
- GeoGebra: \(ax^n+bx+c\):
- Enter ax^n [space]+bx+c
Complete the Square for \(ax^2+bx+c\)
- GeoGebra: CompleteSquare(\(ax^2+bx+c\)):
- Enter cs(ax^2 [space]+bx+c)
Factor \(ax^n+bx+c\)
- GeoGebra: Factor(\(ax^n+bx+c\)):
- Enter factor(ax^n [space]+bx+c)
(CAS only) CFactor \(ax^n+bx+c\)
- GeoGebra: CFactor(\(ax^n+bx+c\)):
- Enter cfactor(ax^n [space]+bx+c)
(CAS only) Solve \(ax^n+bx+c\)
- GeoGebra: Solve(\(ax^n+bx+c\)):
- Enter solve(ax^n [space]+bx+c)
(CAS only) CSolve \(ax^n+bx+c\)
- GeoGebra: CSolve(\(ax^n+bx+c\)):
- Enter csolve(ax^n [space]+bx+c)

Derivative of \(y= ax^n+bx+c\)
- GeoGebra: Derivative(\(ax^n+bx+c\)):
- Enter d/dx[space](ax^n+bx+c)
  (Be sure to include parentheses around the expression!)
Tangent of \(y= ax^m+bx+c\) at x = n
- GeoGebra: Tangent(m,\(ax^n+bx+c\)):
- Enter \tngnt(m, ax^n+bx+c) (or \tangent(m, ax^n+bx+c))
Integral of \(y=ax^n+bx+c\) between 0 and m
- GeoGebra: Integral(\(ax^n+bx+c\),0,m):
- Enter \int_0[space]^m[space][space][space](ax^n[space][space][backspace]+bx+c)[space][space]dx
  (Be sure to include parentheses around the expression!)

Table of \(y= \frac{\left(x\pm \sqrt(5x^2+4)\right)}{2}\)
This is sometimes called the Fibonacci Function - study the table of values to see why...
- GeoGebra: (x+sqrt(5*x^2+4))/2:
- Enter \table(x+\sqrt(5*x^2[space]+4[space][space])/2[space] or just (x+\sqrt(5*x^2[space]+4[space][space])/2[space] and tap the View Table button.
3D Graph of \(y^2=x^2+xy+1\)
For a different view of the Fibonacci Function, set GeoGebra Perspective to T for this...
- GeoGebra: Try Solve(y^2=x^2+x*y+1,y):
- Enter y^2=x^2+x*y+1

(Graph Input only) Stat Plots: BoxPlot
- GeoGebra: BoxPlot(5,1,{0,0,1,1,1,2,2,3,3,3,4,5,5}):
- Enter boxplot(5,1,{0,0,1,1,1,2,2,3,3,3,4,5,5})
(Graph Input only) Stat Plots: DotPlot
- GeoGebra: DotPlot({0,0,1,1,1,2,2,3,3,3,4,5,5}):
- Enter dotplot({0,0,1,1,1,2,2,3,3,3,4,5,5})
(Graph Input only) Stat Plots: BarChart
- GeoGebra: BarChart({0,1,2,3,4,5}, {2,3,2,3,1,2}):
- Enter barchart({0,1,2,3,4,5}, {2,3,2,3,1,2})
(Graph Input only) Stat Plots: FrequencyPolygon
- GeoGebra: FrequencyPolygon({-0.5,0.5,1.5,2.5,3.5,4.5,5.5}, {2,3,2,3,1,2}):
- Enter FrequencyPolygon({-0.5,0.5,1.5,2.5,3.5,4.5,5.5}, {2,3,2,3,1,2})
(Graph Input only) Stat Plots: StemPlot
- GeoGebra: StemPlot({0,0,1,1,1,2,2,3,3,3,4,5,5}):
- Enter stemplot({0,0,1,1,1,2,2,3,3,3,4,5,5})