[b][size=150]The quadratic function is [color=#ff0000]y = x[sup]2[/sup][/color] , denoted by function g. [br][br][/size][/b]The transformed basic function is [b][color=#ff0000]y = a(x - h)[sup]2[/sup] +k[/color][/b][br][b][color=#ff0000][size=150][br]Note[/size][/color][/b]: The 'slider' feature on the x-y coordinate plane can be used to change the [color=#ff0000][b]a, h, and k[/b][/color] values [br] for the following exercises. To do so, place the cursor and hold it on the dot of the slider and [br] slide it to the desired m and b values.[br] To move the slider to a different location on the x-y plane, place the cursor and hold it on the line [br] of the slider and move it to the desired location.[br][br][b][color=#ff00ff]Note: You can zoom in or out with the mouse.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br]The new function is [b][color=#ff0000]y=x[sup]2 [/sup]+ 3[/color][/b] , denoted by function f(x).[br]Find the the vertex of f(x).[b][color=#ff00ff][br]Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down. [br] [br][/b] The new function is [b][color=#ff0000]y=x[sup]2[/sup] - 3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1.[br] Set h=0 since there is no horizontal shift [br] Set k= - 3 which represents the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][br][/size][/b][b]Horizontal shift of 3 units to the right. [br][br][/b] The new function is [b][color=#ff0000]y=(x-3)[sup]2[/sup][/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1.[br] Set h=3 which represents the horizontal shift of 3 units to the right. [br] Set k=0 since there is not vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[br][/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Horizontal shift of 3 units to the left. [br][br][/b] The new function is [b][color=#ff0000]y=(x+3)[sup]2[/sup][/color] [/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1.[br] Set h=- 3 which represents the horizontal shift of 3 units to the left. [br] Set k=0 since there is not vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up plus a horizontal shift of 3 units to the right. [br][br][/b] New function: [b][color=#ff0000]y = (x-3)[sup]2[/sup] +3[/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1.[br] Set h=3 which represents the horizontal shift of 3 units to the right. [br] Set k=3 which represents the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][br][/size][/b][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the left. [br][br][/b] New function: [b][color=#ff0000]y = (x+3)[sup]2[/sup] - 3 [/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=1. [br] Set h=- 3 which represents the horizontal shift of 3 units to the left. [br] Set k=- 3 which represents the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units down plus a horizontal shift of 3 units to the right. [br][br][/b] New function: [b][color=#ff0000]y = (x - 3)[sup]2[/sup] - 3 [/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=1.[br] Set h= 3 which represents the horizontal shift of 3 units to the right. [br] Set k=- 3 which represents the vertical shift of 3 units down.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up plus a horizontal shift of 3 units to the left. [br][br][/b] New function: [b][color=#ff0000]y = (x + 3)[sup]2[/sup] + 3 [/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=1.[br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which represents the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Vertical stretch by a factor of 3.[br][br][/b] New function: [color=#ff0000] [b]y = 3 x[sup]2[/sup][/b] [/color] , denoted by function f.[br][br] [color=#0000ff]Set a=3. [br] Set h= 0 since there is no horizontal shift.[br] Set k= 0 since there is no vertical shift.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][br][/size][/b][b]Vertical shrink by a factor of 1/3.[br][br][/b] New function: [b][color=#ff0000]y = 1/3 x[sup]2[/sup][/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=1/3. [br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which represents the vertical shift of 3 units up.[br][br][/color][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Vertical shift of 3 units up, horizontal shift of 3 units to the left [br] and a vertical stretch by a factor of 2 . [br][br][/b] New function: [b][color=#ff0000]y = 2(x + 3)[sup]2[/sup] + 3 [/color][/b], denoted by function f.[br][br] [color=#0000ff]Set a=2. [br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][br][/size][/b][b]Vertical shift of 3 units up, horizontal shift of 3 units to the left, [br] a vertical shrink by a factor of 1/2 . [br][br][/b] New function: [b][color=#ff0000]y = 1/2(x + 3)[sup]2[/sup] + 3 [/color][/b], denoted by function f.[br] [color=#0000ff]Set a=2.[br][br] Set h= - 3 which represents the horizontal shift of 3 units to the left. [br] Set k= 3 which [/color]represents [color=#0000ff]the vertical shift of 3 units up.[br][/color][br][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[b][size=150]Perform the following quadratic function transformation:[br][/size][/b][br][b]Reflection over the x-axis. [br][br][/b] New function: [b][color=#ff0000]y = - x[sup]2[/sup] [/color][/b] , denoted by function f.[br][br] [color=#0000ff]Set a=-1. [br] Set h= 0 since there is no horizontal shift.[br] Set k= 0 since there is no vertical shift.[br][br][/color][b][color=#ff00ff] Observe the transformation of the quadratic function.[/color][/b]

[br][b]Discuss [/b]the effect of different values of [color=#ff0000][b]a, h and k [/b][/color] on the graph of [math]f\left(x\right)=a\left(x-h\right)^2+k[/math].[br]

How well did you understand the math in this lesson?[br]How did you feel about this lesson?[br]Reflect on the math from this lesson.