/ \ 1=- -<+-3 j=cas. +c-o. Introduction to Quadratic Relations. Student Handout Unit 3 Lesson 1

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$Graph / \ Linear Relations Nonlinear Relations ie following chart compares of relations that are linear vs nonlinear Introduction to Quadratic Relations constant$ Equation, t N) Graph U The graph is a parabola Quadratic Relations The following chart shows some of the properties of a quadratic relation table of values shows that

Equation, t N) Graph U The graph is a parabola Quadratic Relations The following chart shows some of the properties of a quadratic relation table of values shows that

$differences in the table are The first differences in the table are not 7 4 4 5 3 6 ( /\ E Table of Values \ evles constant (all the same) all the same None of the$

1 Graph / \ Linear Relations Nonlinear Relations ie following chart compares of relations that are linear vs nonlinear Introduction to Quadratic Relations constant constant but the second differences are The first differences in the table are not e X e Table of Values squared The equation has one variable that is Equation, t N) Graph U The graph is a parabola Quadratic Relations The following chart shows some of the properties of a quadratic relation table of values shows that the second differences are all constant quadratic relation has the shape of a parabola, the equation involves one of the variables being squared and the The first differences in the table are The first differences in the table are not ( /\ E Table of Values \ evles constant (all the same) all the same None of the variables have eponents The variables may have eponents or Equation = +co <+3 j=cas The graph is a straight line The graph is not a straight line other functions Student Handout Unit 3 Lesson

) Determine which of the following ate eamples of quadratic functions a) y=+ y= c) y=+3 d) y=() +3 ) Determine

5 37 3 57 I 37 4 5 y 5 E curve of best fit Does this represent a quadratic 4) When a rocket firework is set

2 ) Determine which of the following ate eamples of quadratic functions a) y=+ y= c) y=+3 d) y=() +3 ) Determine the value ofy by subbing in = 3 Day I y fit Does this represent a quadratic relation? 5) When a golf ball is hit the height of the ball is measured for the first 9 seconds Drw the curve of best I y 5 E curve of best fit Does this represent a quadratic relation? 4) When a rocket firework is set off the height of the rocket is measured for the first 6 seconds Draw the a) y=+ y= +I c) y=() d) y= + 3) Determine which of the following are eamples of quadratic functions Unit: Quadratic Relations MFM P

3 y I I II I y y= +4, 3 y=3 4, c) 3 a) y=+ 7 Complete the table of values and graph the relation y c) a) 6) Determine which of the following tables of values are eamples of quadratic functions :f:ll y

Student Handout Unit 3 Lesson Complete the eperiments below using linking cubes and record your

there is one blob of mould today, then there will be 4 tomorrow, 9 the net day, 6 the net day,

side length and the number of cubes What type of relationship do you think eists between the

Eperiment B Jenny wants to build a square pool for her pet iguana She plans to buy tiles to

total play area to the side length of the pool, using linking cubes Purpose Find the

What type of relationship do you think eists between the side length and the play area?

using the cubes Note: The pool is the shaded square, the tiles are white Build the net model in

a curve of best fit Side Number Lentjof Cubes Complete the table, including first and second

4 Student Handout Unit 3 Lesson Complete the eperiments below using linking cubes and record your results in the space provided Eperiment A A particular mould grows in the following way: If there is one blob of mould today, then there will be 4 tomorrow, 9 the net day, 6 the net day, and so on Model this relationship using linking cubes Purpose Find the relationship between the side length and the number of cubes What type of relationship do you think eists between the side length and the number of cubes? Eperiment B Jenny wants to build a square pool for her pet iguana She plans to buy tiles to place around the edge to make a full play area for her pet Model the relationship, comparing total play area to the side length of the pool, using linking cubes Purpose Find the relationship between the side length of the pool (shaded inside square) and the total play area What type of relationship do you think eists between the side length and the play area? Build the following sequence of models, using the cubes Build the following sequence of models using the cubes Note: The pool is the shaded square, the tiles are white Build the net model in the sequence Complete the table, including first and second differences Make a scatter plot and a curve of best fit Side Number Lentjof Cubes Complete the table, including first and second differences Make a scatter plot and a line of best fit Length Total, Play Area First Ditfererides Second Difference Student Handout Unit 3 Lesson Build the net model in the sequence e 3 5 : m r r rr

Purpose Student Handout Unit 3 Lesson tomorrow, and 6 the net day A particular mould grows in the following way: If there is one blob of mould today, then there

Complete the table, including first and second differences HHHHH number of cubes?

What type of relationship do you think eists between the number of cubes in the bottom row and the total Purpose ground floor increases She wants to know how

square Model this relationship, using linking cubes Find the relationship between the number of cubes in the bottom row and the total number of cubes Build the

the sequence Make a plot scatter a and curve of best fit Number of cubes Total in the, Number Bottom ofcl4beu Rqw Dlfference I I I I I Numbcr lot T,piai I the

5 Purpose Student Handout Unit 3 Lesson tomorrow, and 6 the net day A particular mould grows in the following way: If there is one blob of mould today, then there will be 3 Find the relationship between the number of cubes in the bottom row and the total number of cubes Model this relationship using linking cubes 5: Complete the table, including first and second differences HHHHH number of cubes? What type of relationship do you think eists between the number of cubes in the bottom row and the total number of cubes? What type of relationship do you think eists between the number of cubes in the bottom row and the total Purpose ground floor increases She wants to know how many apartments can be built in this design as the number of apartments on the Luisa is designing an apartment building in a pyramid design Each apartment is a square Model this relationship, using linking cubes Find the relationship between the number of cubes in the bottom row and the total number of cubes Build the following sequence of models using the cubes Build the following sequence of models using the cubes Build the net model in the sequence Build the net model in the sequence Make a plot scatter a and curve of best fit Number of cubes Total in the, Number Bottom ofcl4beu Rqw Dlfference I I I I I Numbcr lot T,piai I the Cbe Number :ff I Boffom fqtiles First Row Differences c second Difference including first Complete the Make table, a plot and a second of fit differences scatter and curve best 6 First Differences S 6 I I I I I I I I I I DHIHHHH Eperiment Eperiment C Student Handout Unit 3 Lesson

$I _ \JlJLo),ootball After the team scores a touchdown, the football is kicked b; to the ci )pposing team The quadratic function y = 49 If metres, of the football after seconds + models thec ght, y,$ I i I I I I D I I U at seconds, can be modelled by the function y = 49 I o a) What is the height of the basketball when the player takes the shot?

I i I I I I D I I U at seconds, can be modelled by the function y = 49 I o a) What is the height of the basketball when the player takes the shot?

6 I _ \JlJLo),ootball After the team scores a touchdown, the football is kicked b; to the ci )pposing team The quadratic function y = 49 If metres, of the football after seconds + models thec ght, y, in 3 (Ti C) t\) a) What is the maimum height of the football? V o At what time does the football reach its maimum height? i c For what time interval is the height of the football greater than 5 m? I i I I I I D I I U at seconds, can be modelled by the function y = 49 I o a) What is the height of the basketball when the player takes the shot? I Cl) C 3 Basketball A basketball player takes a shot The height of the ball, y, in metres, = I I I D O What is the maimum height reached by the ball? D?V C c) What is the height of the bail s after it is thrown? I I + During what time interval is the height of the ball greater than 3 m? C d) )) I e) If it takes 63 s for the basketball to reach the hoop, how high is the hoop? Cl) Cl) < D = H ) 4 W, D Cl) Cl) Cl) J Q o 4 Flares Red mini flares are used by some boaters in emergency situations The u 3 / a height of a flare above water, when fired at an angle of 7 to the horizontal, can be modelled by the function y = 49 is the time, in seconds, since the flare was fired I a) What is the maimum height of the flare? 3 How many seconds does it take for the flare to reach its maimum height D c) For how many seconds does the flare burn before it hits the water? Cl) y is the height, in metres, and y is the I U) 4 d) During what time intervals is the flare less than m from the water? 5 Cl) Ci) C) C) C 5 Symphony of Fire The Symphony D of Fire is the largest offshore C fireworks competition in the world D The fireworks are C) launched from barges anchored I $ô in Lake Ontario, close to downtown Toronto The C) () fireworks are synchronized with C) a musical soundtrack The path D C) Cl) of one type of rocket at the ) Symphony of Fire is described by C), m,t the function _ I, = y = 49 C height of the rocket, in metres, 5 and is the time, in seconds, D Cl) D since the rocket was fired a) What is the maimum height 5 Cl) reached by the rocket? How o many seconds after it is fired D D does the rocket reach this o height? Cl) How high is the rocket above the lake when it is fired? c) For how long is the rocket in 4kt? Cl) D D

a) y=4+5 y= 4 c) y=sin d) (8 marks) State whether the following relations are linear,

L How long is the arrow at least 3m above the ground?

$/ 7 / \ \ \ What height is the arrow after 5 seconds? When is the arrow m above the ground?$ $/ \ / What is the initial height of the arrow? 8 6?$

7 a) y=4+5 y= 4 c) y=sin d) (8 marks) State whether the following relations are linear, quadratic or neither 3 When does the arrow hit the ground? L How long is the arrow at least 3m above the ground? At what time does the maimum height occur? / 7 / \ \ \ What height is the arrow after 5 seconds? When is the arrow m above the ground? / 7 \ \\ What is the maimum height of the arrow? / \ / What is the initial height of the arrow? 8 6? :f ijh: 3 y= +3 3, I I I I ::zl H 3 (6 marks) Plot the following function using the tables of values provided g) f) d) c) e) a) (8 marks) The graph below shows the height, in meters, of an arrow being shot into the air versus time, in seconds 7 N 4l \J 3 4 e) f) g) h) Assessment and Evaluation: Unit 3 Lesson

8.1.1: Going Around the Curve

8.1.1: Going Around the Curve Experiment A A particular mould grows in the following way: If there is one blob of mould today, then there will be 4 tomorrow, 9 the next day, 16 the next day, and so on.