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Raziskovavnje parametrov polinomov

Zgled

Graf polinoma tretje stopnje f(x) = a x³ + b x² + c x + d katerega koeficiente lahko spreminjamo z drsniki. Poleg tega so prikazane ničle in ekstremi polinoma.

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Navodila

1.f(x)Vnesi f(x) = a*x³ + b*x² + c*x + d v vnosno polje v prikazu Algebr in vnos potrdi z Enter.
Namigt: GeoGebra bo avtomatsko ponudila ustvarjanje drsnikov za koeficiente a, b, c, in d.
2.Toolbar ImageSkrij drsnike v Grafičnem prikazu s klikom krogca na levi strani vnosa v algebrskem oknu.
3.Toolbar ImageUse the sliders in the Algebra View in order to change the values of the parameters to a = 0.2, b = -1.2, c = 0.6 and d = 2.
4.Root[f] Enter R = Root[f] in order to display the roots of the polynomial and automatically name them R1, R2, and R3.
5.Extremum[f] Enter E = Extremum[f] in order to display the local extrema of the polynomial.
6.Toolbar ImageUse tool Tangent in order to create the tangents to the polynomial through the extrema E1 and E2
Hint: Open the Toolbox of special lines and select the tool Tangent. Successively select point E1 and the polynomial in order to create the tangent. Repeat for point E2.
6.Toolbar ImageSystematically change the values of the sliders in order to explore how the parameters affect the polynomial.