Graph a cubic polynomial [code]f(x) = a x³ + b x² + c x + d[/code] whose parameters can be changed using sliders. In addition, display the roots and local extrema with their corresponding tangents.

[table][tr][td]1.[/td][td][code]f(x)[/code][/td][td]Enter [code]f(x) = a*x³ + b*x² + c*x + d[/code] into the[i] Input[/i] [i]Bar [/i]and hit the [i]Enter [/i]key.[/td][/tr][tr][td][/td][td][/td][td][b]Hint:[/b] [i]GeoGebra [/i]will automatically create sliders for the parameters [i]a[/i], [i]b[/i], c, and [i]d[/i]. [/td][/tr][tr][td]2.[/td][td][icon]https://www.geogebra.org/wiki/uploads/thumb/1/1f/Algebra_shown.svg/32px-Algebra_shown.svg.png[/icon][/td][td]Show the sliders in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] by selecting the disabled [img width=20,height=21]https://lh6.googleusercontent.com/Ou4lDYXXsgee93x0NpUhAJl5h3lQ_PRGBbiZs0wiRR_92LfhK-OdV7S_kcvLBte9LFhclo0SS63rJ5yBh7pPRUk52N2F8NnkjTOuP_ScuYGU_grYTNG3WUCyMPSSrPimllsJDRi1[/img] [i]Visibility [/i]buttons on the left of the corresponding entries in the [img width=16,height=16]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i].[/td][/tr][tr][td]3.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Use the sliders in the [img]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/16px-Menu_view_graphics.svg.png[/img] [i]Graphics View[/i] to change the values of the parameters with the [i]Move [/i]tool to [code]a = 0.2[/code], [code]b = -1.2[/code], [code]c = 0.6[/code] and [code]d = 2[/code].[/td][/tr][tr][td]4.[/td][td][code]Root(f)[br][/code][br][/td][td]Enter [code]R = Root(f) [/code]into the [i]Input Bar [/i] to display the roots of the polynomial and automatically name them[sub][i] [/i][/sub][i]R[sub]1[/sub], R[sub]2[/sub] [/i]and [i]R[sub]3[/sub][/i].[/td][/tr][tr][td]5.[/td][td][code]Extremum(f)[/code][br][/td][td]Enter [code]E = Extremum(f)[/code] to display the local extrema of the polynomial.[/td][/tr][tr][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_tangent.png[/icon][/td][td]Use the [i]Tangent[/i] tool to create the tangents to the polynomial through the extrema [i]E[sub]1[/sub][/i] and [i]E[sub]2[/sub][/i]. [br][/td][/tr][tr][td][/td][td][/td][td][b]Hint:[/b] Open the [i]Toolbox [/i]of [i]Special Lines[/i] and select the [i]Tangent [/i]tool. Successively select point [i]E[sub]1[/sub][/i] and the polynomial to create the tangent. Repeat for point [i]E[sub]2[/sub][/i].[/td][/tr][tr][td]6.[/td][td][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/td][td]Systematically change the values of the sliders using the [i]Move[/i] tool to explore how the parameters affect the polynomial.[/td][/tr][/table]