01 - Introduction to Quadratic Relations PDF

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1 - Introduction to Quadratic Relations

MPM2D – Introduction to Quadratics

Date: ______________________________________________

Introduction to Quadratic Relations So far: Linear Relationships

New: Quadratic Relationships

Equation: _______________________________

Equation: _______________________________

Max Exponent is: _______

Max Exponent is: _______

 = 2 + 1

 = !

For linear relations, _________________________________________________________________________________ For quadratic relations, _____________________________________________________________________________

Example 1  = −2 ! − 4 + 4

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1 - Introduction to Quadratic Relations

MPM2D – Introduction to Quadratics

Example 2  =  ! − 2 − 3

The direction of opening of the parabola can be determined from the sign of the 2nd difference.

If the 2nd difference is positive, then the parabola opens up.

If the 2nd difference is negative, then the parabola opens down.

Homework 1. Are the following data sets linear relations or quadratic relations or neither? a.

b.

c.

x

y

x

y

x

y

10

21

5

–2

0

0

20

41

6

–3

1

2

30

61

8

–5

2

8

40

81

11

–8

3

18

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1 - Introduction to Quadratic Relations

MPM2D – Introduction to Quadratics

2. What is the degree of each of the following polynomials? a. 3 − 2

b. 2% !

c. 2%

d. −4.9( !

e.  ! + 3 − 1

f.

2 ) − 3 +  − 4

3. The following data represents the average body mass for children up to the age of 12. Child’s Age (years)

1

2

3

4

5

6

Mass (kg)

11.5

13.7

16.0

20.5

23.0

23.0

7

8

9

30.0

33.0

39.0

10 38.5

11 41.0

12 49.5

a. Draw a scatterplot for the data. b. Draw in a line or curve of best fit. c. What type of relationship best fits the data?

4. At the store, Shoe Must Go On, the latest line of shoes is being sold, and the data on the number of sales is shown in the table below. Month

1

2

3

4

5

6

7

8

9

10

Pairs of Shoes Sold

56

60

62

62

60

56

50

42

32

20

a. Draw a scatterplot for the data. Draw in a line or curve of best fit. b. When did the number of shoes sold reach its peak? c. Show that the number of shoes sold each month is a quadratic relationship.

5. A ball is thrown into the air. The height is recorded in the table below Time (seconds)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Height (m)

1.5

3.5

4.9

5.7

5.7

5.2

4.1

2.4

0.1

a. Draw a scatterplot for the data. Draw in a line or curve of best fit. b. What type of model best represents this relationship? c. When is the ball at the highest point?

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1 - Introduction to Quadratic Relations

MPM2D – Introduction to Quadratics

Answers 1. a. linear

b. linear

c. quadratic

2. a. 1 d. 2

b. 2 e. 2

c. 1 f. 3

3.

4.

5.

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1 - Introduction to Quadratic Relations

MPM2D – Introduction to Quadratics

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