TODAY IN CALCULUS…

Warm Up: Factoring Polynomials

Learning Targets : You will find the absolute values of real numbers

and understand the properties of absolute value. You will find the distance between two numbers on

the real number line. You will define intervals on the real number line. You will find the midpoint of an interval and use

intervals to model and solve real-life problems.

Independent practice

WARM UP: Find the solution set of the inequality

Factor the polynomial Calculate the zeros

Draw a number line and test theintervals between the zerosto find where the polynomial will be positive

Define the solution set using intervalnotation

−𝟐−𝟔 𝟎−𝟑−𝟕+¿ +¿−

0.2 DISTANCE ON A REAL NUMBER LINETHREE TYPES OF DISTANCE PROBLEMS:1. The directed distance from a to b

2. The directed distance from b to a

3. The distance between a and b

EXAMPLE: Find (a) the directed distance from -3 to 4, (b) the directed distance from 4 to -3, and (c) the distance between -3 and 4.

𝑎 𝑏

𝑏−𝑎

𝑎−𝑏

𝒃−𝒂

𝒂−𝒃

|𝒃−𝒂|𝒐𝒓 |𝒂−𝒃|

a.

b.

c.

PRACTICE: Find (a) the directed distance from a to b, (b) the directed distance from b to a, and (c) the distance between a and b.

1. 2.

a.

b.

c.

a.

b. c.

0.2 INTERVALS DEFINED BY ABSOLUTE VALUETWO TYPES OF INEQUALITIES INVOLVING ABSOLUTE VALUE:1. 2.

𝑎

𝑑 𝑑

Less th’AND’-Graph will connect

𝑎

𝑑 𝑑

Great’OR’-Graph will go in opposite directions

EXAMPLE: Use absolute values to describe the given interval (or pair of intervals) on the real number line.

1. 2.

𝑎

𝑑 𝑑

𝑎

𝑑 𝑑

Less th’AND’ graph

𝟑 𝟑

𝟎Great’OR’ graph

−3 3 20 24𝟐𝟐

𝟐 𝟐

PRACTICE: Use absolute values to describe the given interval (or pair of intervals) on the real number line.

1. 2.

𝑎

𝑑 𝑑

𝑎

𝑑 𝑑

Less th’AND’ graph

𝟑 𝟑

−𝟒Great’OR’ graph

−7 −1 −3 3𝟎

𝟐 𝟐

EXAMPLE 2: Use absolute values to describe the given interval (or pair of intervals) on the real number line.

1. All numbers more than five units from 2.

𝑎

𝑑 𝑑

𝑎

𝑑 𝑑

Great’OR’ graph

𝟓 𝟓

𝟐Less th’AND’ graph

𝒄

𝒉 𝒉

PRACTICE: y is less than h units from c

Less th’AND’:

Interval notation:

EXAMPLE 3: Solve the inequality and sketch the graph of the solution on the real number line.

1. 2.

−3 0

1−−1 −1

Great’OR’: or Interval notation:

𝑎+¿ +𝑎+𝑎

PRACTICE: Solve the inequality and sketch the graph of the solution on the real number line.

1. 2.

Less th’AND’:

Interval notation:

−3 3

Great’OR’: or Interval notation:

−1 −1−1

0.2 INTERVALS DEFINED BY ABSOLUTE VALUETO FIND THE MIDPOINT:

Given the endpoints c and d

EXAMPLE: Find the midpoint of the given intervals:a) b)

∙22

0.2 INTERVALS DEFINED BY ABSOLUTE VALUE

PRACTICE: Find the midpoint of the given intervals:a) b)

∙33

HOMEWORK #2:

Pg.12: 3-31odd, 35-43odd, 44, 45

If finished, work on other assignments:

HW #1: Pg. 7: 5-35odd