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©2002 Alice Keeler

Definition of a quadratic function

Plotting Quadratics

Example #2 plotting quadratics

Example #3

A is negative

Practice problems

Vertex

Axis of Symmetry

Examples Axis of Symmetry

Using the axis of symmetry

©2002 Alice Keeler

Knowledge

Comprehension

Application

Synthesis

Analysis

Evaluation

©2002 Alice Keeler

Whenever you simplify you must use order of operations.

Order of Operations is a 4 step process!

1. Parenthesis

2. Exponents

3. Multiply or Divide

4. Add or Subtract

Simplify:3(3 + 7)2 5 P E M/D A/S

3(3 + 7)2 5 Start with parenthesis, do what is inside of the parenthesis first.

3(10)2 5 P E M/D A/S

Next calculate any exponents.3(10)2 5

3(100) 5 P E M/D A/S

3(100) 5 First come first serve, multiply or divide

300 5 P E M/D A/S

300 5 Still more multiplying or dividing

60

Simplify:27 3(5 – 3)2 P E M/D A/S

27 3(5 – 3)2 Start with parenthesis, do what is inside of the parenthesis first.

27 3(2)2 P E M/D A/S

Next calculate any exponents.27 3(2)2

27 3(4) P E M/D A/S

27 3(4) First come first serve, multiply or divide

9(4) P E M/D A/S

9(4) Still more multiplying or dividing

36

36 3 (6 – 4)2 – 4

36 3 (2)2 – 4

36 3 (4) – 4

36 3 (4) – 4

12 (4) – 4 48 – 4

5 32 – 6 + 2[14 – 3(2)]

5 32 – 6 + 2[14 – 3(2)]Note that [ ] brackets are parenthesis, they are useful when you need parenthesis around parenthesis. You can use [ ] or ( ) as is convenient.

With parenthesis (brackets) you need to start order of operations all over again! P E M/D A/S

5 32 – 6 + 2[14 – 3(2)]

P E M/D A/S Inside of the brackets there is not parenthesis or exponents so go straight to the multiply or divide

5 32 – 6 + 2[14 – 3(2)]

5 32 – 6 + 2[14 – 6]

5 32 – 6 + 2[8]

5 32 – 6 + 2(8)

If you prefer parenthesis to brackets, you can trade them.

5 32 – 6 + 2(8)

5 32 – 6 + 2(8)

Now that you are done with the parenthesis, move onto exponents

5 32 – 6 + 2(8)5 9 – 6 + 2(8)

5 9 – 6 + 2(8)

5 9 – 6 + 2(8)

45 – 6 + 2(8)

45 – 6 + 2(8)

45 – 6 + 16

45 – 6 + 16

39 + 16

212 2 36

8 2 2

NOTE: When you encounter a fraction there are

INVISIBLE parenthesis around the numerator and the denominator!!!

212 2 36

8 2 2

Invisible parenthesis!

212 2 36

8 2 2

In order of operations P E M/D A/S

first do what is inside of the parenthesis. What this means in this

problem is first simplify the numerator, then simplify the

denominator

212 66

8 2 2

266

8 2 2

now simplify the denominator

266

8 2 2

266

4 2

266

8

REMEMBER: Fractions are division! Now that you have taken care of the parenthesis P E M/D A/S move onto

exponents!

266

8

6

368

REMEMBER: Fractions are division! To divide six eighths you will simply reduce!

336

4 You will need a common denominator

to add three fourths to 36

3 36

4 1

3 36 4

4 1 4

3 144

4 4

147

4

                                                            

115 – 10 2 (32 + 1) =

65

•g

8[62 – 3(2+5)] 8 + 3=

18

•g

5 + (4 8)

37

•g

(40 4) – (9 – 5)

6

•g

32 8 + 3 7 – 6

19

•g

(5 + 2)2 3 – 4 + 5 2

153

•g

(8 – 3)(12 4) – 5

10

•g

3(23 + 42)

72

•g

(6 + 8)(8 – 3) (9 + 3 – 2)2

0.7

•g

39

•g150 (17 5)2

6(0.2 + 0.3) – 0.25

2.75

•g

0

•g28 6(4) 42(5)

31

2(6 2) 3 916

2

•g2 2

36 4 22(3 2)

3(3 + 7)2 5

60

•g

7 5 – 3 4

23

•g

27 3(5 – 3)2

36

•g

53 – 8 5 + 6

91

•g

(5 + 3) 2 + 2

6

•g

6 (12 – 7.5) – 7

20

•g

(3 + 6) 32

1

•g

125 [5(2 + 3)]

5

•g

Common mistake: Order of Operations is a 4 step process, often people mistake it for a 6 step process.

Multiply and Divide are considered EQUAL! This means first come first serve (left to right).

Addition and Subtraction are considered EQUAL! This means first come first serve (left to right).

You are going to be given a problem.

Person 1 starts with the problem and does anything that is inside of parenthesis

Person 2 does any exponents

Person 3 does any Multiplication or Division as is comes left to right

Person 4 does any addition or subtraction as it comes left to right

When person 4 has the answer stand up.

First: Parenthesis

Second: Exponents

Third: Multiply and Divide left to right

Fourth: Add and Subtract left to right

(STAND UP)

115 – 10 2 (32 + 1) =

65

•g

8[62 – 3(2+5)] 8 + 3=

18

•g

5 + (4 8)

37

•g

(40 4) – (9 – 5)

6

•g

32 8 + 3 7 – 6

19

•g

(5 + 2)2 3 – 4 + 5 2

153

•g

(8 – 3)(12 4) – 5

10

•g

3(23 + 42)

72

•g

(6 + 8)(8 – 3) (9 + 3 – 2)2

0.7

•g

39

•g150 (17 5)2

6(0.2 + 0.3) – 0.25

2.75

•g

0

•g28 6(4) 42(5)

39

2(6 2) 3 916

2

•g2 2

36 4 22(3 2)

3(3 + 7)2 5

60

•g

7 5 – 3 4

23

•g

27 3(5 – 3)2

96

•g

53 – 8 5 + 6

91

•g

(5 + 3) 2 + 2

6

•g

6 (12 – 7.5) – 7

20

•g

(3 + 6) 32

1

•g

125 [5(2 + 3)]

5

•g

In order of operations there are 4 steps!!!

Please Excuse My Dear Aunt Sally

Common Mistake: NOT six steps only FOUR

5 + (2 + 4)2 4 • 3

5 + (6)2 4 • 3

5 + 36 4 • 3

5 + 9 • 35 + 27

32

7 – 2 + 6 2 3

7 – 2 + 3 37 – 2 + 9

5 + 914

s + 3

s

Find the perimeter

26

s + 3

s

Find the area

40

When you substitute a variable for a number use PARENTHESIS

3 3

2 2

x y

x y

x = 2 and y = 3

When you substitute a variable for a number use PARENTHESIS

3 3

2 2

x y

x y

x = 3 and y = 2

3 3

2 2

(3) (2)

(3) (2)

27 8

9 4

35

5