1. U4D11 Have out: Bellwork: 4 4 total: Solve for x. a) b) c)
Assignment, pencil, red pen, highlighter, textbook, calculator, GP notebook
U4D11
Have out:
Bellwork:
total:
Solve for x. a) b) c) +1 4 4 +1
x2 –8x = 4
+ 16
+ 16 +1
(x – 4)2 = 20 +1 +1 +1 +2 +1 +2 +1

2. Absolute Value Add to your notes: absolute value:
the distance a number is from zero on a number line. Since distance is nonnegative, the absolute value of a number is always nonnegative.
Symbol: | |
|4|
= 4
|–4|
= 4
Example: -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
Given the function f(x) = | x |, evaluate the following values:
a) f(–6)
b) f(13) c)
d) f(–π)
e) f(0)
f) f(n)
= | –6 |
= | 0 |
= | 13 |
= | –π |
= | n |
= 6
= 0
= 13
= π

3. Solving Absolute Value Equations
PG – 115
Solving Absolute Value Equations
For what values of x does:
a) | x | = 8
b) | x | = 4
c) | x | = –4
x = –8, 8
x = –4, 4
No Solution
These are quick, but let’s solve more complicated problems.

4. Solving Absolute Value Equations
Add to your notes:
Step:
Example #1:
1) Write two equations and “drop” the absolute values.
|x + 1| = 6
x + 1 = 6
x + 1 = – 6
2) Solve each equation.
– 1
– 1
– 1
– 1
x = 5
x = – 7

5. Solving Absolute Value Equations
Add to your notes:
Step:
Example #2:
1) Isolate the absolute value.
4 |x – 3| + 2 = 22
– 2
– 2
4 |x – 3| = 20 4 4
2) Write two equations and “drop” the absolute values.
|x – 3| = 5
x – 3 = 5
x – 3 = – 5
3) Solve each equation.
+ 3
+ 3
+ 3
+ 3
x = 8
x = –2

6. PARENT GRAPH TOOLKIT Name: Absolute Value x y -3 -2 -1 1 2 3 x y
PG – 114
PARENT GRAPH TOOLKIT y x 2 4 –2 –4 8 6 10 –6 –8
–10
Name:
Absolute Value x y -3 -2 -1 1 2 3 x y
Parent Equation:
y = | x |
Description of Locator:
(–1, 1)
(1, 1)
vertex
(h, k)
(0, 0)
General Equation:
y = a|x – h| + k
Properties:
open up or down
horizontal shift
Domain:
Range:
y = +/- a|x – h| + k
{x| x  R}
{y| k ≤ y < }
Wider or narrower
(-, )
[k, )
vertical shift

7. Based on the patterns you have observed, graph the next 6 absolute value functions on the worksheet WITHOUT using a graphing calculator. 2 4 6 8 10 y x –2 –4 –6 –8
–10

8. Finish today's worksheet

9. old slides

10. PG – 113
a) Investigate y = | x |. Be sure to graph the function and include all the elements of a function investigation.
y = | x | 2 4 –2 –4 6 8 –6 –8 x y x y –4 –3 –2 –1 1 2 3 4 4
x–intercept:
(0, 0) 3
y–intercept:
(0, 0) 2
domain:
(-, ) 1
range:
[0, )
asymptotes:
None 1 2 3 4

11. PG – 113
b) Take out your Parent Graph Toolkit. Do you think that any of the equations you already have is the parent of y = | x |? Why or why not?
None of them are the parent graphs for y = | x | since their graphs are completely different.
It sort of looks like a parabola, but the absolute value function is “V” shaped and does not have a curved vertex like the graph of a parabola.
c) How can we change the equation y = | x | to move it up, down, left, or right? How can we stretch it or compress it, or make it open down? Write a general equation for y = | x |.
y = a|x – h| + k

12. PG – 116
c) Make a sketch of f(x) = |x + 1| and use the graph to show why there are two answers. Identify on your graph what two x–values give a corresponding y–value of 6.
f(x) = |x + 1| 2 4 –2 –4 6 8 –6 –8 x y
Shift left 1 unit.
y = 6
(–7, 6)
(5, 6)
|x + 1| = 6

13. PG – 117
Graph f(x) = |x – 3| and x = 3 on the same set of coordinate axes. Write a description of the relationship between the two graphs.
The graph x = 3 is the line of symmetry for the graph of f(x) = |x – 3|.
x = 3
f(x) = |x – 3| 2 4 –2 –4 6 8 –6 –8 x y
Shift right 3 units