Create a linear function with sliders and intersect it with a quadratic function.[br][br]Explore the construction and learn how to create a function with parameters and how to intersect two functions with [i][url=https://www.geogebra.org/graphing]GeoGebra Graphing Calculator[/url][/i]. Then try it yourself by following the instructions below.

[table][tr][td]1.[/td][td][/td][td]Enter the linear function [math]f(x)=a\cdot x+b[/math] into the [i]Input Bar[/i]. Sliders for variables [i]a[/i] and [i]b[/i] will be created automatically.[/td][/tr][tr][td]2.[/td][td][/td][td]Enable the [img]https://wiki.geogebra.org/uploads/thumb/3/34/Algebra_hidden.svg/16px-Algebra_hidden.svg.png[/img] [i]Visibility [/i]button next to the sliders to show them in the [i]Graphics View.[/i][br][/td][/tr][tr][td]3.[/td][td][/td][td]Change the values of the sliders for [i]a [/i]and [i]b [/i]and explore how the graph of [i]f(x) [/i]adapts to your changes.[br][/td][/tr][tr][td]4.[/td][td][/td][td]Create a quadratic function by entering [math]g\left(x\right)=x^2[/math] into the [i]Input Bar.[/i][/td][/tr][tr][td]5.[/td][td][/td][td]Use the command [math]Intersect\left(f,g\right)[/math] to create the intersection points of [i]f(x) [/i]and [i]g(x). [/i]The intersection points [i]A [/i]and [i]B [/i]are displayed in the [i]Graphics View[/i], while the coordinates of the points are shown in the [i]Algebra View[/i].[/td][/tr][tr][td][/td][td][icon]/images/ggb/toolbar/mode_intersect.png[/icon][/td][td][b]Note:[/b] You may use the [i]Intersect [/i]tool from the [i]Tools View[/i] and select the two functions as well to create the intersection points. [/td][/tr][tr][td]6.[/td][td][/td][td]Move the sliders for [i]a [/i]and [i]b [/i]and explore how the intersection points [i]A [/i]and [i]B [/i]adapt to your changes.[/td][/tr][tr][td]7.[/td][td][img width=24,height=24]https://lh5.googleusercontent.com/EeYLvel9HmsnYD7ZRVm-HBQtblHhlB35cdQzXdG11nyuG3R7BCgnyC_l3L8aKn1R4wNkQnlMJHA72jcGN8n5f2RRahLZMiuy01yMfDJFEssc0gxkkfajbgHSyt1KTilGP0RyH5NA[/img][/td][td]Select the graph of [i]f(x) [/i]and [i]g(x) [/i]and change the color of the function graphs using the [i]Style Bar[/i] to enhance your construction.[/td][/tr][/table]