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.Explore the construction...
Poskusite sami ...
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. | | Skrij drsnike v Grafičnem prikazu s klikom krogca na levi strani vnosa v algebrskem oknu. |
3. | | Use 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. | | Use 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. | | Systematically change the values of the sliders in order to explore how the parameters affect the polynomial. |