Transforming Quadratic Functions Day 2

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1 Name Grade Subject(s) Algebra 9 th Transfrming Quadratic Functins Day Hlly Fischer CONTEXT INFORMATION Lessn Title Transfrming quadratic functins Time 50 minutes LEARNING OUTCOMES A.QE..: Graph quadratic equatins in tw variables with and withut technlgy. Standards AI.QE.7: Describe the relatinships amng the slutins f a quadratic equatin, the zers f the functin, the x- intercepts f the graph, and the factrs f the expressin. Gals Essential Cntent Materials Skill (TWBAT...). Students will be able t write quadratic equatins that have been shifted hrizntally and vertically.. Students will be able t graph quadratic equatins that have been shifted hrizntally and vertically. Vertical Shift (translatin): The graph f the functin f x! + c is the graph f f x! translated vertically. If c > 0, the graph f f x! is translated c units up. If c < 0, then the graph f f x! is translated c units dwn. Graphing calculatr, pencil, paper PROCEDURES Have the students graph each f the fllwing equatins n their graphing calculatrs. Each f these images will create different images. Then discuss with students that nt all graphs are straight lines. By changing different parts f the equatins, we can create different images. y = 6 x! 6 y = 6 x! 6 Hk (- 5 min) y = 9 x! + y = 9 x! + y = 4 x! + y = 4 x! + Discuss with students hw quadratic equatins can be anywhere n the graph. Discuss hw we will discver hw t translate quadratics t different parts f the graph. Befre beginning the lessn split students int grups f tw. Students will then be asked t cmplete the discvery activity. Transfrmatin f the Quadratic Functin (Part A) Graph the quadratic functin y belw:

2 What is the vertex? Did the graph pen up r dwn? Check yur graph n the graphing calculatr. Push the Y= buttn Type in x Push the GRAPH buttn Did yu graph the functin crrectly? The functin + k We are nw ging t lk at what happens when we change the equatin. Nte: Yu are lking at hw the functin transfrms int a new functin. Using yur calculatr Push the Y= buttn Keep Y = the same x G dwn and type the next equatin: Y + 5 Push the GRAPH buttn t view What changed frm the riginal graph? What is the new vertex? Nw have the students repeat the same steps with the fllwing equatins. Have them describe what happened t each and tell what the new vertex is.. Y Y. Y 8

3 Nw ask the students what happens when yu add k t the functin? Can yu write an equatin that wuld mdel the fllwing situatins? Vertically Shift the Functin up Nw have the students write the equatins that mdel the fllwing situatins. Vertically Shift the functin up 8 Vertically Shift the Functin up 0 Vertically Shift the Functin up 0 Vertically Shift the Functin up Nw we have the functin the equatin. k and we are ging t lk at what happens when we change Nte: Yu are lking at hw the functin transfrms int a new functin. Using yur calculatr Push the Y= buttn Keep Y = the same x G dwn and type the next equatin: Y 5 Push the GRAPH buttn t view What changed frm the riginal graph? What is the new vertex? Nw have the students repeat the same steps with the fllwing equatins. Have them describe what happened t each and tell what the new vertex is.. Y. Y. Y 8 Ask them what happens when yu subtract k t the functin? Can yu write an equatin that wuld mdel the fllwing situatins? Vertically Shift the Functin dwn

4 Nw have the students write an equatin that wuld mdel the fllwing situatins? Vertically Shift the functin dwn 8 Vertically Shift the Functin dwn 0 Vertically Shift the Functin dwn 0 Vertically Shift the Functin dwn Nw have the students describe what is happening in each functin belw withut a calculatr. Which way is it shifting and by hw much? Clse ( - 5 min) Use a calculatr t check yur answers * Have the students turn this befre leaving class. Extensin Guided Ntes: Belw. Pg , 4, 5, 7, & 9- SUPPORTING MATERIALS 4

5 Transfrmatin f the Quadratic Functin (Part A) Graph the quadratic functin y belw: What is the vertex? Did the graph pen up r dwn? Check yur graph n the graphing calculatr. Push the Y= buttn Type in x Push the GRAPH buttn Did yu graph the functin crrectly? The functin + k We are nw ging t lk at what happens when we change the equatin. Nte: Yu are lking at hw the functin transfrms int a new functin. Using yur calculatr Push the Y= buttn Keep Y = the same x G dwn and type the next equatin: Y + 5 Push the GRAPH buttn t view What changed frm the riginal graph? What is the new vertex? 5

6 Repeat the same steps with the fllwing equatins. Describe what happened and tell the new vertex.. Y. Y. Y What happens when yu add k t the functin? Can yu write an equatin that wuld mdel the fllwing situatins? Vertically Shift the Functin up Vertically Shift the functin up 8 Vertically Shift the Functin up 0 Vertically Shift the Functin up 0 Vertically Shift the Functin up 6

7 The functin f (x) k We are nw ging t lk at what happens when we change the equatin. Using yur calculatr Push the Y= buttn Keep Y = the same x G dwn and type the next equatin: Y 5 Push the GRAPH buttn t view What changed frm the riginal graph? What is the new vertex? Repeat the same steps with the fllwing equatins. Describe what happened and tell the new vertex.. Y. Y. Y 8 What happens when yu subtract k t the functin? Can yu write an equatin that wuld mdel the fllwing situatins? Vertically Shift the Functin dwn Vertically Shift the functin dwn 8 Vertically Shift the Functin dwn 0 Vertically Shift the Functin dwn 0 7

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3.1 QUADRATIC FUNCTIONS IN VERTEX FORM

3.1 QUADRATIC FUNCTIONS IN VERTEX FORM PC0 T determine the crdinates f the vertex, the dmain and range, the axis f symmetry, the x and y intercepts and the directin f pening f the graph f f(x)=a(x p) +