Explore the impact of parameters on a quadratic polynomial by either moving the function graph or changing its equation.

[table][tr][td][size=100]1.[/size][/td][td][icon]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/120px-Menu_view_algebra.svg.png[/icon][/td][td][size=100]Type [code]f(x) = x^2[/code] into the[i] Input[/i] [i]Bar [/i]and hit the [i]Enter[/i] key.[br]Which shape does the function graph have?[/size][/td][/tr][tr][td][size=100]2.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/size][/td][td][size=100]Use the [i]Move[/i] tool and select the function. Click on the [img width=16,height=12]https://lh4.googleusercontent.com/9kckeXCdJGBgMCEHMVsq_b-7Sj3EpBus_T7dXQUGJNNxQ_GWiLHpW_OO6POOqmYiaaaW-4r9lLac11lt9IfNaxs-RhbG19waa1-alNcYjFfs3MEtYltRBhiDMGZfEYh2deQp6cci[/img] [i]Style Bar[/i] and select [img width=27,height=27]https://lh4.googleusercontent.com/qo523vBe2kp06yE5TSzbf5veSz_CV34lt_euYe2WGK6ewHItOP38C0w2vW_ivGhlTw7peLuSMPp14_EiQQZCuqjM2NishFBqoT8zXa0BygW9_FRs9nThmzGWLtSAmsZXmJbzWBh2[/img] to unfix the function and to be able to drag the function 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] and watch how the equation in the [img]https://wiki.geogebra.org/uploads/thumb/4/40/Menu_view_algebra.svg/16px-Menu_view_algebra.svg.png[/img] [i]Algebra View[/i] adapts to your changes.[/size][/td][/tr][tr][td][size=100]3.[/size][/td][td][size=100][icon]https://wiki.geogebra.org/uploads/thumb/c/c8/Menu_view_graphics.svg/120px-Menu_view_graphics.svg.png[/icon][/size][/td][td]Change the function graph so that the corresponding equation matches [br][list][*][i]f(x) = (x + 2)²[/i][/*][*][i]f(x) = x² - 3[/i], and [/*][*][i]f(x) = (x - 4)² + 2[/i].[br][/*][/list][/td][/tr][tr][td][size=100]4.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/size][/td][td][size=100]Select the equation of the polynomial. Use the keyboard to change the equation to [code]f(x) = 3 x^2[/code]. How does the function graph change?[br][/size][/td][/tr][tr][td][size=100]5.[/size][/td][td][size=100][icon]https://www.geogebra.org/images/ggb/toolbar/mode_move.png[/icon][/size][/td][td][size=100]Repeat changing the equation by typing in different values for the parameter (e.g. 0.5, -2, -0.8, 3).[/size][/td][/tr][/table]