Parameters of a polynomial
Task
Graph a cubic polynomial
f(x) = a x³ + b x² + c x + d whose parameters can be changed using sliders. In addition, display the roots and local extrema with their corresponding tangents.Explore the construction...
Instructions
| 1. | f(x) | Enter f(x) = a*x³ + b*x² + c*x + d into the Input Bar and hit the Enter key. |
| | | Hint: GeoGebra will automatically create sliders for the parameters a, b, c, and d. |
| 2. |  | Show the sliders in the  Graphics View by selecting the disabled  Visibility buttons on the left of the corresponding entries in the  Algebra View. |
| 3. |  | Use the sliders in the Graphics View to change the values of the parameters with the Move tool to a = 0.2, b = -1.2, c = 0.6 and d = 2. |
| 4. | Root(f)
| Enter R = Root(f) into the Input Bar to display the roots of the polynomial and automatically name them R1, R2 and R3. |
| 5. | Extremum(f)
| Enter E = Extremum(f) to display the local extrema of the polynomial. |
| 6. |  | Use the Tangent tool to create the tangents to the polynomial through the extrema E1 and E2. |
| | | Hint: Open the Toolbox of Special Lines and select the Tangent tool. Successively select point E1 and the polynomial to create the tangent. Repeat for point E2. |
| 6. | | Systematically change the values of the sliders using the Move tool to explore how the parameters affect the polynomial. |