yr+9.6+Graphing+Quadratic+Expressions

Features of a quadratic function, plotting points to draw quadratic graphs, Sketching parabolas of different forms of quadratic equations eg. turning point form. |||||| ** VOCABULARY: ** axis of symmetry, parabola, dilation(width), reflection, translation(shift), maximum, minimum, turning point, vertex. || eso – every second one CLASSPAD - graphics calculator || ** Classroom Activities ** || ** Consolidation Tasks ** || ** Enrichment & Extension Activities ** || ** Homework ** || Students will sort, connect and make sense of information given to solve a mystery question || ** “Does Amelie make it to the Catwalk” ** Investigation ||  ||   || ** “Does Amelie make it to the Catwalk” ** Investigation || Students will identify what the key features of a parabola are, and by answering specific questions they will show their understanding of each feature || **__ Quiz, Quiz, Trade __** Activity
 * STUDENT PLANNER 2012 ** **__Topic: QUADRATIC GRAPHS__** (Chapter 11) **NAME:**
 * ** In this topic you will explore the following concepts **
 * || // Abbreviations //
 * ** 0 ** || ** Learning Outcome **
 * ** 1 ** || ** Learning Outcome – **
 * Key features of the quadratic graph **

Worked Examples || Ex 11A Q1-6 ||  || 12B Key Features of parabolas worksheet (4 questions) || Students will apply their knowledge of substitution to obtain the co-ordinates of enough points to draw a parabola || Skillsheet 11.2 (Substitution practice)
 * ** 2 ** || ** Learning Outcome **
 * Plotting points to draw graphs of quadratic functions **

Pg 457 Ex 11B Q1, Q2ab || Puzzle 10.4 || Pg 457 Ex 11B Q4-6 || Homework Sheet || Student will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph (links lessons 4, 5, 6, 7)
 * ** 3 ** || ** Learning Outcome – **
 * Investigation of Quadratic Graphs **

First transformation: What happens when we introduce a coefficient for x2? || ** Year 9 Mathematics Task Booklet **
 * This can be done interspersed with the text work or as a whole to be consolidated with the exercises ** || Summary Notes

Make your own parabola (y=x2) template to help you sketch them

Graphing grids also available

Pg 460 Ex 11C Q1- 5 || P461 Ex 11C Q7-10 || 30 minutes to catch up on exercises, worksheets and review work || Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
 * ** 4 ** || ** Learning Outcome – Investigation continued **

Second transformation: Parabolas of the form y=ax2 + c What happens when a constant is added to x2 || ** Year 9 Mathematics Task Booklet **
 * This can be done interspersed with the text work or as a whole to be consolidated with the exercises ** || Summary Notes

Pg 464 Ex 11D Q1, 2, 3, 4, 5, Q6adf,7, 8 || P466 Ex 11D Q9-12 || CH 12 Quadratic Functions 2 worksheet

** PTO ** || Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
 * ** 5 ** || ** Learning Outcome – Investigation continued **

Third transformation: Parabolas of the form y=(x – h)2 What happens when a constant is added/subtracted before squaring? || ** Year 9 Mathematics Task Booklet **
 * This can be done interspersed with the text work or as a whole to be consolidated with the exercises ** || Summary Notes

P468 Ex 11E Q1, 2, 3, 4, 5, 6, 7, 8 || P469 Ex 11E Q9, 10 || 30 minutes to catch up on exercises and review work || Students will use the ClassPad (or ClassPad Manager on netbooks) to sketch graphs and in doing so will come to recognise the different transformations of the quadratic graph
 * ** 6 ** || ** Learning Outcome – Investigation continued **

Combining all transformation: Parabolas of the form y=(x – h)2 + c || ** Year 9 Mathematics Task Booklet **
 * This can be done interspersed with the text work or as a whole to be consolidated with the exercises ** || Summary Notes

P468 Ex 11F Q1, 2, 3 ESO, 4, 5, || P474 Ex 11F Q 6-8 || __ Worksheet __ : What do you know about the parabola? || Students will determine the x-intercepts, y-intercepts and turning points to sketch parabolas in the form y = (x + m) (x + n) || Sketching Quadratic Graphs (type 1,2 &3) sheets
 * ** 7 ** || ** Learning Outcome – Sketching Parabolas in the Factorised Form **

Worked examples || Pg477 Ex 11G Q1 ace, 2 ESO || P474 Ex 11G Q 3 || 30 minutes to catch up on exercises and review work || Students will apply what they learnt to solve practical problems || Worked examples P479 Ex 11H Q 1-5 ||  || P479 Ex 11H Q6-8 ||   || Students will manipulate the 3 different forms of a quadratic equation || Worksheet: Revision- Different forms of a Quadratic Expression. || ** Time Rider Task Featuring Laura Craft ** ||  || Chapter Review and Own Revision || ** [Nine Work-Station Activities] ** ||  ||   ||   ||   || Practice TEST ||  ||   || Own Revision ||
 * ** 8 ** || ** Learning Outcome – Applications **
 * ** 9 ** || ** Learning Outcome **
 * 3 Different Forms of a Quadratic Equation **
 * ** 10 ** || ** TASK CENTRE ACTIVITY **
 * ** 11 ** || ** Catch up lesson & Revision ** || Chapter Review p483
 * ** 12 ** || ** Assessment – Test ** ||  ||   ||   || Organise notebook, ready for next topic ||


 * Different Forms of a Quadratic Expression **


 * This sheet is designed to show how it is possible to move between the different forms of a Quadratic Expression **


 * * Use FOIL to move between Expanded Form & Factorised Form: **


 * * Use Sums & Products to move between Factorised Form to Expanded Form: **


 * * Use the Completing the Square process to change from Expanded Form to Turning Point Form: **


 * * Use FOIL again to move from Turning Point Form to Expanded Form: **

|| ** FACTORISED FORM ** ( x + 4 ) ( x + 6 ) ** use ** FOIL to expand ||   x² + 6x + 4x + 24 = x² + 10x + 24  || || S= -7 & P=10 ( x - 2 ) ( x - 5 )  ||  ** Given ** x² - 7x + 10 ** use ** Sums & Products  || || x² - 8x + 15 ** Use ** completing the square process  ||   x² - 8x + 15 = x² - 8x **+ 16 - 16** + 15 = ( x - 4 ) ² - 1 ||  = x² + 10x + 16   ||  ** Given ** ( x + 5 ) ² - 9 ** Expand ** the brackets & collect like terms ||
 * ** EXPANDED FORM ** ||  ** TURNING POINT FORM **  ||
 * [[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]][[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]]** Given **
 * [[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]][[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]] Want two numbers whose
 * [[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]][[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]] || ** Given **
 * [[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]][[image:http://mrwallisscience.wikispaces.com/site/embedthumbnail/placeholder?w=200&h=50 width="200" height="50"]] ||  x² + 10x + 25 - 9

Fill in the gaps in the table and hence discover the different forms of the same quadratic expression: || ** FACTORISED FORM ** || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || ||
 * ** EXPANDED FORM ** ||  ** TURNING POINT FORM **  ||
 * ( x - 7 ) ( x - 5 )
 * ||  x² - 10x + 21
 * ( x + 3 ) ( x - 9 )
 * ||  x² + 4x + 3
 * ||  x² - 10x + 9
 * ( x - 3 ) ( x - 5 )
 * || ||  ( x + 7 ) ² - 4
 * || ||  ( x - 4 ) ² - 36
 * ( x - 3 ) ( x + 1 )
 * x ( x + 6 )  || || ||
 * ||  x² + 4x - 12
 * || ||  ( x - 2 ) ² - 64
 * ||  x² - 10x
 * ( x - 2 ) ( x + 4 )
 * || ||  ( x - 3 ) ² - 1
 * ||  x² - 4x - 32

|| ** FACTORISED FORM ** ||  x² - 12x + 35   ||   ( x - 6 ) ² - 1   || ||  x² - 10x + 21 ||  ( x - 5 ) ² - 4   || ||  x² - 6x - 27   ||   ( x - 3 ) ² - 36   || ||  x² + 4x + 3   ||   ( x - 2 ) ² - 1   || ||  x² - 8x + 15   ||   ( x - 4 ) ² - 1   || ||  x² + 14x + 45   ||   ( x + 7 ) ² - 4   || ||  x² - 8x - 20   ||   ( x - 4 ) ² - 36   || ||  x² - 2x - 3   ||   ( x - 1 ) ² - 4   || ||  x² + 4x - 12   ||   ( x - 2 ) ² - 16   || ||  x² - 4x - 60   ||   ( x - 2 ) ² - 64   || ||  x² - 10x   ||   ( x - 5 ) ² - 25   || ||  x² + 2x - 8   ||   ( x - 1 ) ² - 9   || ||  x² - 6x + 8   ||   ( x - 3 ) ² - 1   || ||  x² - 4x - 32   ||   ( x - 6 ) ² - 1   ||
 * ANSWERS………….. **
 * ** EXPANDED FORM ** ||  ** TURNING POINT FORM **  ||
 * ( x - 7 ) ( x - 5 )
 * ( x - 3 ) ( x - 7)
 * ( x + 3 ) ( x - 9 )
 * ( x + 1 ) ( x + 3 )
 * ( x - 1 ) ( x - 9 )  ||   x² - 10x + 9   ||   ( x - 5 ) ² - 16   ||
 * ( x - 3 ) ( x - 5 )
 * ( x + 5 ) ( x + 9 )
 * ( x + 2 ) ( x - 10 )
 * ( x - 3 ) ( x + 1 )
 * x ( x + 6 )  ||   x² + 6x   ||   ( x + 3 ) ² - 9   ||
 * ( x - 2 ) ( x + 6 )
 * ( x + 6 ) ( x - 10 )
 * x ( x - 10 )
 * ( x - 2 ) ( x + 4 )
 * ( x - 2 ) ( x - 4 )
 * ( x + 4 ) ( x - 8 )