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Mitchell District High School MPM 2D Principles of Mathematics Unit 5: Quadratic Functions Unit Goals: 1) I can explain, manipulate and provide an example of a function. 2) I can transform and graph a quadratic function, using completing the square when necessary. 3) I can use my understanding of quadratic functions and apply them to real-world situations. # Topic Goal Practice Questions Questions to Ask About 1 What is a Function? I know what a function is and how to determine domain and range of relationships. Page 197 #1, 2-5eop 6-10, 14, 17, 18, 20 a)c)e) 22 2 Transformations of Quadratic Functions I know how to alter the equation of a parabola in order to transform it on a grid. Page 222 #1-4, 9, 10, 11, 12, 13 3 Graphing Using Transformations I can use transformations of quadratic functions to graph Parabolas. Page 222 #(1-3)eop, 6, 7, (9,10)eop 4 Completing the Square I can switch the equation of a parabola from Standard Form, to Vertex form in order to graph the parabola. Page 234 #(1-9)eop + handout 5 Finite Differences I know what finite differences are and how you can use them to tell the difference between Linear and Quadratic relations. Page 242 from text 6 Applications of parabolas – Part 1 I can apply what we know about parabolas to models of "real life" situations. Page 224 #8, 11, 14, 15 Page 236 # 14, 16, 17, 22 7 Applications of parabolas – Part 2 I can set up equations and complete the square for maximum and minimum problems. Page 235 #10, 11, 12ace, 15, 19, 24, 27 Additional questions Page 235 #16, 29, 21, 22 8 Parabolas of Best Fit I can find the equation of a parabola if given a set of points or I can find a best fit parabola by hand or with a graphing calculator. Page 246 -247 Parts 1, 2 & 3

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Page 1: MPM 2D - PBworks

Mitchell District High School

MPM 2D Principles of Mathematics

Unit 5: Quadratic Functions Unit Goals:

1) I can explain, manipulate and provide an example of a function.

2) I can transform and graph a quadratic function, using completing the square when necessary.

3) I can use my understanding of quadratic functions and apply them to real-world situations.

# Topic Goal Practice

Questions Questions to Ask About

1 What is a Function? I know what a function is and how to determine domain and range of

relationships.

Page 197 #1, 2-5eop 6-10, 14, 17, 18, 20 a)c)e) 22

2 Transformations of Quadratic Functions

I know how to alter the equation of a parabola in order to transform it

on a grid.

Page 222 #1-4, 9, 10, 11, 12,

13

3 Graphing Using Transformations

I can use transformations of quadratic functions to graph

Parabolas.

Page 222 #(1-3)eop, 6, 7,

(9,10)eop

4 Completing the Square

I can switch the equation of a parabola from Standard Form, to Vertex form in order to graph the

parabola.

Page 234 #(1-9)eop + handout

5 Finite Differences

I know what finite differences are and how you can use them to tell

the difference between Linear and Quadratic relations.

Page 242 from text

6 Applications of parabolas – Part 1

I can apply what we know about parabolas to models of "real life"

situations.

Page 224 #8, 11, 14, 15

Page 236 # 14, 16, 17, 22

7 Applications of parabolas – Part 2

I can set up equations and complete the square for maximum

and minimum problems.

Page 235 #10, 11, 12ace, 15,

19, 24, 27 Additional questions

Page 235 #16, 29, 21, 22

8 Parabolas of Best Fit

I can find the equation of a parabola if given a set of points or I can find a best fit parabola by hand

or with a graphing calculator.

Page 246 -247 Parts 1, 2 & 3

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Page 19: MPM 2D - PBworks

Al Gebra Completes the Square

The Evil Dr. Gebra (Al Gebra) will stop at nothing to rid the world of math related humour. He’s once again stolen the punch lines to a set of jokes and coded them behind some complicated

mathematics.

You are the key to unlocking these punch lines.

He left behind this set of quadratic functions. We believe that if you found the maximum or minimum value of each parabola, that will complete the cipher so that you can decipher the

punch lines. Record the maximum or minimum value in the table provided and then see if your answers match mine. Once we have agreed upon our answers we can proceed to decipher

the code.

Good Luck! We’re counting on you! !

A)

y = x2 +10x +12! B)

y = x2 +12x + 30! C)

y = −x2 + 4x + 3 ! D)

y = 2x2 +16x +17 !E)

y = −4 x2 − 40x − 75 ! F)

y = 5x2 +100x + 492 ! G)

y = −12x2 + 8x − 29 ! H)

y =14x2 + 2x − 6!

I)

y = 0.1x2 + 0.6x − 4.1! J)

y = −13x2 − 4x ! K)

y = 10x2 −160x + 658 ! L)

y =17x2 + 2x + 8!

M)

y = −x2 +18x − 70 ! N)

y = 42x2 − 84x + 33! O)

y = −19x2 +114x −165 ! P)

y = 0.75x2 + 9x +10 !Q)

y = −0.01x2 + 0.1x + 4.75 ! R)

y = −4 x2 −16x −12 ! S)

y =15x2 + 4x −10 ! T)

y = −7x2 + 56x −104 !U)

y = x2 +14x + 29 ! V)

y =19x2 + 4x + 45! W)

y = 2x2 − 24x + 74 ! X)

y = 5x2 + 30x + 38 !Y)

y = −13x2 − 6x − 3! Z)

y = −9x2 − 36x −14 ! ! !!!!

Record'the'maximum/minimum'value'of'each'parabola'here…'

A ! B ! C ! D !

E ! F ! G ! H !

I ! J ! K ! L !

M ! N ! O ! P !

Q ! R ! S ! T !

U ! V ! W ! X !

Y ! Z ! ! !

Page 20: MPM 2D - PBworks

Al Gebra Completes the Square

1. What did the little acorn say when he grew up?

3,25,6,11,25,8,4,24 2. How many calories are in a piece of chocolate pi? -13,-17,-17,4,6,-7,-5,11,-13,8,25,1,24 8,-10,4,25,25 -17,6,-5,-9,8

6,-9,25 -8,6,-20,4 3. How do you catch a Geometrysaurus Rex? 2,-5,8,-10 -13 22,6,-5,-15 8,4,-13,-17. 8,-10,25

-30,-13,11,25 2,-13,24 24,6,-20 8,4,-13,-7 -13 22,6,-5,-15 4. There are three types of math students in this world… … 8,-10,6,-30,25 2,-10,6 7,-13,-9 7,6,-20,-9,8 -13,-9,-15

8,-10,6,-30,25 2,-10,6 7,-13,-9’8 5. Why don’t you do math in the jungle 25,9,25,4,24 8,-5,11,25 -30,6,11,25,6,-9,25 -13,-15,-15,-30

-8,6,-20,4 -17,1,-20,-30 -8,6,-20,4 8,-10,25,24 3,25,8 -13,8,25

Page 21: MPM 2D - PBworks

MPM 2D U5L6 Applications of Parabolas Part 1

Applications of ParabolasMany things in life follow a quadratic model.

All projectiles move in a parabolic path in regards to space and time.

Financial situations can also have a parabolic model applied to them.

Example 1. An angry bird is shot at a pig. Its height h above the pig, in metres, after t seconds can be modelled by...

h = -4.9(t - 2)2 + 29

a) What was the maximum height reached by the bird?

b) When did it reach maximum height?

c) How much higher than the pig was the sling shot that launched the bird?

d) How long does it take before the bird kills the pig?

Topic : applications of parabolas

Goal : to apply what we know about parabolas to models of "real life" situations.

Page 22: MPM 2D - PBworks

MPM 2D U5L6 Applications of Parabolas Part 1

HomeworkPage 224 #8, 11, 14, 15 Page 236 # 14, 16, 17, 22

Example 2. A punter kicks a football. It's height h, in metres, after t seconds is

h = -4.9t2 +22.54t + 1.1

Remember you don't know anything about maximum and minimum values until you have a completed square.

a) What was the maximum height reached by the football?

b) When did it reach maximum height?

c) What was the height of the ball when the punter kicked it?

d) How long is the ball in the air?

Keighsee
Page 23: MPM 2D - PBworks

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Page 24: MPM 2D - PBworks

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Keighsee
Page 25: MPM 2D - PBworks

MPM 2D U5L8 Parabolas of Best Fit

Topic : parabolas of best fit

Goal : I can find the equation of a parabola if given a set of points or I can find a best fit parabola by hand or with a graphing calculator.

Parabolas of Best FitIf you have a set of points, how can you figure out the equation of the parabola they came from? Take the following set for instance...

But not all quadratic relationships are perfect. Especially if we are modelling a "real life" situation. Take the following statistics on the height of a baseball vs. time.

Height of a Baseball after being hit

Time(s) 0 1 2 3 4 5 6Height(m) 2 27 42 48 43 29 5

Page 26: MPM 2D - PBworks

MPM 2D U5L8 Parabolas of Best Fit

Keighsee
See DESMOS video on how to use technology to find the Parabola of Best FitThere are no notes for that video - the main things you need to remember are the two formulas you need to plug into DESMOSRecord them belowStandard form : _____________________________Vertex form : ________________________________Remember that the subscript you use must match your table of values and the R-value given tells you how good your fit is. The closer it is to 1, the better.
Page 27: MPM 2D - PBworks

Quadratic Functions 1. State the domain and range of each of the given relations.

a) b) c) d)

D: { } D: { } D: { } D: { } R: { } R: { } R: { } R: { }

e) { (0,4) (1,3) (6,8) (7,11) (2,8) } D: { } R: { } f) { (4,3) (7,8) (3,-2) (4,6) (7,8) } D: { } R: { } 2. State the equation of each parabola a) has a vertex of (3, -6) ____________________________ b) congruent to

y =12x2 with x=7 as the axis of symmetry and a maximum value of 4 ____________________

c) stretched by 3 and shifted up 5 ____________________________ 3. Find the value of ‘k’ if

y = 4x2 + k passes through (-1,-1) 4. Complete the following table for the given parabolas. Graph each parabola.

Vertex Axis of Symmetry Max/Min Value Range

a)

y =12x2 + 2

b)

y = −2(x − 3)2

c)

y = (x + 4)2 − 6

d)

y = −14(x +1)2 + 3

e)

y = −3x2 +10 5. Complete the square for each of the following, then state the vertex, axis of symmetry, max/min value and

range for each. a)

y = 0.5x2 + 6x − 3 b)

y = x2 +10x + 7 c)

y = −4 x2 − 24x −12 d)

y = −13x2 +10x + 5

6. Find the x and y-intercepts of the following parabolas.

a)

y = 2(x + 3)2 − 32 b)

y = 3(x − 5)2 + 7 c)

y = 5(x +1)2 + 2 d)

y = −12x2 +10

Keighsee
Review
Page 28: MPM 2D - PBworks

7. Find the x and y-intercepts of

y = 5x2 +10x − 3 8. Explain how finite differences in a table of values can tell you whether a relations is linear, quadratic or neither. 9. Use finite differences to determine if the following tables represent linear or quadratic relations (or neither).

x y x y 0 7 2 -5 1 9 4 -11 2 15 6 -17 3 25 8 -23

10. The path of a thrown ball can be represented by

h = −0.004d 2 + 0.112d +1.6 where h is the height of the ball in metres, and d is the horizontal distance, in metres, from the person who threw the ball.

a) How HIGH was the ball when the thrower first releases it? b) What is the MAXIMUM height of the ball? c) What is the HORIZONTAL DISTANCE the ball has travelled when it reaches its maximum height? 11. Tickets for a show at the children’s theatre cost $5 and the 120 seats in the theatre are filled daily. Added

expenses mean that the theatre owner has to increase the cost of tickets, but a survey shows that for each $0.50 increase in ticket cost, they will sell 10 fewer tickets to each show. Based on these statistics, what ticket price do you recommend in order to maximize their revenue?

12. An apple orchard now has 80 trees and each tree on average produces 400 apples. For each additional tree

planted the average number of apples per tree drops by 4. How many additional trees need to be planted to maximize the number of apples (yield) produced each year in the orchard?

13. Creasyn and Morgan are knitting scarves to sell at the craft show. The wool for each scarf costs $6. They were

planning to sell the scarves for $10 each, the same as last year when they sold 40 scarves. However, they know that if they raise the price, they will be able to make more profit, even if they end up selling fewer scarves. They have been told that for every 50¢ increase in the price, they can expect to sell four fewer scarves. What selling price will maximize their profit and what will the profit be?

14. An electronics store sells an average of 60 entertainment systems per month at an average of $800 more than

the cost price. For every $20 increase in the selling price, the store sells one fewer system. What amount over the cost price will maximize profit?

15. Arnold has 24 m of fencing to surround a garden, bounded on one side by the wall of his house. What are the

dimensions of the largest rectangular garden that he can enclose? 16. Jamie throws a ball that will move through the air in a parabolic path due to gravity. The height, h, in metres, of

the ball above the ground after t seconds can be modelled by the function

h = 4.9t 2 + 40t +1.5 a) Find the zeros of the function and interpret their meaning. b) Determine the time needed for the ball to reach its maximum height. c) What is the maximum height of the ball?

Keighsee
See the website for a full set of solutions to this review