Algebra 2 Unit 1- Absolute Value Equations/Inequalities

Question 1

What is the general shape of an absolute value when graphed?

Answer 1

A ‘V’

2 rays extending from a vertex

Question 2

> (Graphed)

Answer 2

Dashed, shaded above

Question 3

<
(Graphed)

Answer 3

Dashed, shaded below

Question 4

≥
(Graphed)

Answer 4

Solid, Shaded above

(Think, there’s a solid line below it so it is graphed as a solid)

Question 5

≤
(Graphed)

Answer 5

Solid, Shaded below
(Think, there’s a solid line below it so it is graphed as a solid)

Question 6

What does ‘a’ tell us?

Answer 6

If a>1, vertical stretch (narrower)
If 0<a<1, vertical compression (wider)
If ‘a’ is negative, reflection across the x-axis

A is the slope of the rays (sides)

Example: -2/3|x|
1. Reflection across the x-axis (-)
2. Vertical compression (2/3 factor)

Question 7

What does ‘h’ tell us?

Answer 7

Horizontal shift, shifts opposite of the sign
i.e. +=- -=+

Example: |x+7|
1. Shift left 7 units

Question 8

What does ‘k’ tell us?

Answer 8

Vertical shift, true to the sign
i.e. +=+ -=-

Example: |x|-3
1. Shift down 3 units

Question 9

How to solve Absolute Value Equations?

Answer 9

1. Isolate the absolute value expression
2. Create two equations: 1 will look exactly the same and 1 will have a negative sign applied to the side without the absolute value expression
3. Drop the absolute value symbols and solve both
4. Check your answers!!!

Question 10

How to solve Absolute Value Inequalities?

Answer 10

1. Isolate the absolute value expression
2. Create two inequalities: 1 will look exactly the same and 1 will have a negative sign applied to the side without the absolute value expression
3. Drop the absolute value symbols and solve both
4. Write your answer in interval or set notation

Question 11

What is ‘Extraneous Solution’?

Answer 11

A solution that results in a false statement when checked.

Question 12

<
(Inequality)

Answer 12

an AND solution
Between numbers

Example: -1<x<7

Question 13

≤
(Inequality)

Answer 13

an AND solution
Between numbers

Example: -6 ≤ x ≤14

Question 14

> (Inequality)

Answer 14

an OR solution
Smaller or bigger than a number

Example: x<15 or x> 25

Question 15

≥
(Inequality)

Answer 15

an OR solution
Smaller or bigger than a number

Example: x≤ -1/2 or x≥ 4

Question 16

How to solve for X-intercepts?

Original equation: y= -|x-24|-16

Answer 16

Replace y with zero and solve to get x

The x-intercepts in this equation are none.

Question 17

How to solve for Y-intercepts?

Original equation: y= -|x-24|-16

Answer 17

Replace the x with zero and solve to get y

The y-intercept in this equation is -40.

Question 18

How to find axis of symmetry?

Original equation: y= -|x-24|-16

Answer 18

It is your h, opposite of the sign.

The axis of symmetry in this equation is 24.

Question 19

What do Interval Notations use?

Answer 19

Parentheses () or Brackets []
Parenthesis mean < or >
Brackets mean ≤ or ≥
Can Mix and Match
Uses infinity symbol
Uses the Symbol ‘U’ to show gaps

Example:
(-3, 15]

Question 20

What do Set Notations use?

Answer 20

Uses Inequality symbols
{x|x ∈ ℝ}
“x such that x is an element of the real number set”
{x|x > 3}
“x such that x is greater than 3”
Uses the word or to show gaps
Example:
{x|-3<x≤ 15}

Question 21

Range: (-4,-1,0,2,2)

What could you do instead?

Answer 21

(-4,-1,0,2)

You don’t need to add the second 2, there’s already a 2.