Download Graphing Absolute Value Functions

1. {(0, 10), (2, 7), (4, 5), (6, 2),
(10, 1) }
a. Make a scatter plot
b. Describe the correlation
c. Write the equation of the line
of best fit
b. Negative correlation
c. (0, 10) & (4, 5)
𝒚𝟐 − 𝒚𝟏 𝟓 − 𝟏𝟎 −𝟓
𝑚=
=
=
= −𝟏. 𝟐𝟓
𝒙𝟐 − 𝒙𝟏
𝟒−𝟎
𝟒
y = -1.25x + 100
Tues
9/29
Learning Objective:
To graph absolute value
functions
Lesson Hw: Pg. 111 #9 - 15, *31,
2–7
*34, 39 - 42
Algebra II
 To
graph absolute value functions
 Absolute
Value Function
y= 𝑥
 Vertex
– a maximum or minimum
point of the graph
y=𝑎 𝑥−ℎ +𝑘
 Axis
Vertex (h, k)
of Symmetry – a vertical line
that divides a graph
symmetrically
x=h
 Find
the vertex
 Make a table, go two numbers
above and below the x-value of
the vertex. Plug in to find y-value
 The y-values SHOULD reflect over
the vertex if you found the vertex
correctly
 DO NOT ASSUME you have the
correct vertex
Vertex: (0, 0)
Axis of Sym: x = 0
x
y
-2
-1
V(0
1
2
2
1
0)
1
2
𝐲=
𝐲=
𝐲=
𝐲=
−𝟐 = 𝟐
−𝟏 = 𝟏
𝟏 =𝟏
𝟐 =𝟐
Vertex: (0, 0)
Axis of Sym: x = 0
x
y
-2
-1
V(0
1
2
4
2
0)
2
4
𝐲 = 2 −𝟐 = 𝟒
𝐲 = 𝟐 −𝟏 = 𝟐
𝐲=2𝟏 =𝟐
𝐲=2𝟐 =𝟒
𝟏
𝐲 = −𝟐 = 𝟏
𝟐
𝟏
𝐲=
Vertex: (0, 0)
Axis of Sym: x = 0
x
-2
-1
V(0
1
2
y
1
0.5
0)
0.5
1
𝐲=
𝟏
𝟏
𝟏 =
𝟐
𝟐
𝟐
−𝟏 =
𝟏
𝟐
𝟏
𝐲= 𝟐 =𝟏
𝟐
Vertex: (0, 0)
Axis of Sym: x = 0
x
-2
-1
V(0
1
2
y
-2
-1
0)
-1
-2
𝐲=−
𝐲=−
𝐲=−
𝐲=−
−𝟐 = −𝟐
−𝟏 = −𝟏
𝟏 = −𝟏
𝟐 = −𝟐
Vertex: (0, -4)
Axis of Sym: x = 0
x
-2
-1
V(0
1
2
y
-2
-3
-4)
-3
-2
𝐲=
𝐲=
𝐲=
𝐲=
−𝟐 − 𝟒 = −𝟐
−𝟏 − 𝟒 = −𝟑
𝟏 − 𝟒 = −𝟑
𝟐 − 𝟒 = −𝟐
Vertex: (3, 0)
Axis of Sym: x = 3
x
1
2
V(3
4
5
y
2
1
0)
1
2
𝐲=
𝐲=
𝐲=
𝐲=
𝟏−𝟑
𝟐−𝟑
𝟒−𝟑
𝟓−𝟑
=𝟐
=𝟏
=𝟏
=𝟐
𝐲=
𝐲=
𝐲=
Vertex: (-2, 3)
𝐲=
Axis of Sym: x = -2
x
-4
-3
V(-2
-1
0
y
5
4
3)
4
5
−𝟒 + 𝟐 + 𝟑 = 𝟓
−𝟑 + 𝟐 + 𝟑 = 𝟒
−𝟏 + 𝟐 + 𝟑 = 𝟒
𝟎+𝟐 +𝟑=𝟓
𝐲 = − −𝟒 + 𝟐 + 𝟑 = 𝟏
𝐲 = − −𝟑 + 𝟐 + 𝟑 = 𝟐
𝐲 = − −𝟏 + 𝟐 + 𝟑 = 𝟐
Vertex: (-2, 3)
𝐲=− 𝟎+𝟐 +𝟑=𝟏
Axis of Sym: x = -2
x
-4
-3
V(-2
-1
0
y
1
2
3)
2
1
Vertex: (2, 3)
Axis of Sym: x = 2
x
0
1
V( 2
3
4
y
5
4
3)
4
5
𝐲=
𝐲=
𝐲=
𝐲=
−𝟎 + 𝟐 + 𝟑 = 𝟓
−𝟏 + 𝟐 + 𝟑 = 𝟒
−𝟑 + 𝟐 + 𝟑 = 𝟒
−𝟒 + 𝟐 + 𝟑 = 𝟓
7. 𝐲 = 𝒙 + 𝟐 + 𝟑
8. 𝐲 = − 𝒙 + 𝟐 + 𝟑
9. 𝒚 = −𝒙 + 𝟐 + 𝟑
Vertex: (3, -5)
Axis of Sym: x = 3
x
1
2
V( 3
4
5
y
1
-2
-5)
-2
1
𝐲=3 𝟏−𝟑 −𝟓=𝟏
𝐲 = 𝟑 𝟐 − 𝟑 − 𝟓 = −𝟐
𝐲 = 3 𝟒 − 𝟑 − 𝟓 = −𝟐
𝐲=3 𝟓−𝟑 −𝟓=𝟏
𝐲 = −4 −𝟏 − 𝟏 + 𝟓 = −𝟑
𝐲 = −4 𝟎 − 𝟏 + 𝟓 = 𝟏
Vertex: (1, 5)
Axis of Sym: x = 1
x
-1
0
V( 1
2
3
y
-3
1
5)
1
-3
𝐲 = −4 𝟐 − 𝟏 + 𝟓 = 𝟏
𝐲 = −4 𝟑 − 𝟏 + 𝟓 = −𝟑
Vertex: (0, 0)
Axis of Sym: x = 0
x
-2
-1
V( 0
1
2
y
2
1
0)
1
2
𝐲=
𝐲=
𝐲=
𝐲=
−(−𝟐) =2
−(−𝟏) =1
−𝟏 =1
−𝟐 =2
 Your
friend says that the graphs
of y = −3𝑥 and y = −3 𝑥 are
identical. Graph each function and
explain why your friend is not
correct.