10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
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Unit 10
Quadratics
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10.1 Graphing
Absolute Value
and Quadratic
Equations in
Vertex Form
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10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
Algebra: Transformations of Functions
Lesson Objectives
Algebra: Transformations of Functions
Lesson Objectives
Standards
Lesson Notes
F.IF.4
F.IF.7
A.REI.10
F.IF.4
F.IF.7
F.IF.7
A.CED.2
F.BF.1
Standards
Lesson Notes
I will identify the vertex of an absolute value graph
I will graph an absolute value function in vertex form using the vertex
I will sketch a quadratic function using the vertex and slope
I will identify the vertex of a quadratic graph
I will graph a quadratic function in vertex form using the vertex
I will identify the vertex of an absolute value function from an equation and a graph
I will create a quadratic function from a given graph
I will write a quadratic function from a graph into vertex form
10.1 Graphing Absolute Value
and Quadratic Equations in Vertex Form
Algebra: Transformations of Functions
Lesson Objectives
Standards
Lesson Notes
F.IF.4 For a function that models a relationship
between two quantities, interpret key features of
graphs and tables in terms of the quantities, and
sketch graphs showing key features given a verbal
description of the relationship.
F.IF.7 Graph functions expressed symbolically and
show key features of the graph, by hand in simple
cases and using technology for more complicated
cases.
Absolute Value Function
y = a x - h + k
a = slope
if a is positive - graph opens up
if a is negative - graph opens down
if a is bigger than 1 - graph is narrow
if a is smaller than 1 - graph is wide
(h, k) vertex
h is the opposite sign from the equation!
h moves graph left or right
k moves graph up or down
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10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
Absolute Value Function: f(x) =
1. y = 2
+3
What does each letter do to y=
?
a =
Vertex: _______
(h, k) =
mirror
image
h =
k =
opens up if
opens down if
Domain:
Range:
Max or Min?
2. y = ­
3. y =
SE
lin
e
s
Name the vertex for each equation and graph.
Vertex: _______
M
AK
E
es
lin
2
d
st
gi
ri
ra
t
igh
h
ig
t
ra
st
rig
2
id
E
Vertex: _______
3
10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
4. y = 3
Vertex: _______
5. y =
­ 2
Vertex: _______
For QUADRATICS:
Slope only works to get the
FIRST point and only if the
slope is a WHOLE number.
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10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
It's a par
abola!
curvy 2, curvy U
U
y = 2 (x - 5 ) 2 + 4
vertex: (5, 4)
slope: 2
1
Quadratic Function
y = a(x - h)2 + k
a = slope
Only works to get the first set of points
if it is a whole number.
if a is positive - graph opens up
if a is negative - graph opens down
if a is bigger than 1 - graph is narrow
if a is smaller than 1 - graph is wide
(h, k) vertex
h is the opposite sign from the equation!
h moves graph left or right
k moves graph up or down
Sketch the parabola by placing the vertex correctly and
correctly plotting the FIRST point.
6. y = (x + 3)2 – 4
7. y = –2(x – 1)2 + 5
Vertex: _______
Vertex: _______
go up 2
and over 1
in each direction
Only works for 1st set of points!
and only if the slope is a WHOLE number.
5
10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
Sketch the parabola by placing the vertex correctly and
correctly plotting the FIRST point.
8. y = 2(x + 2)2
Vertex: _______
9. y = –(x + 1)2 – 2
Vertex: _______
a) y =
On Your
Whiteboards
Vertex: _______
b) y = ­2
+1
Vertex: _______
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10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
­ 1
d) y = ­
+2
Sketch the parabola by placing the vertex correctly and
correctly plotting the FIRST point.
e) y = (x – 2)2 + 3
Vertex: _______
Vertex: _______
On the
Worksheet
Vertex: _______
f) y = 3(x – 0)2 + 1
Vertex: _______
Homework
Homework
Homework
Hint
c) y =
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
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10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
Name the vertex for each equation and graph.
1. y =
+4
Vertex: _______
5. y =
Vertex: _______
­4
2. y = ­
3. y =
­1
+5
Vertex: _______
4. y = ­
­3
Vertex: _______
Vertex: _______
6. y =
+2
Vertex: _______
7. y = 2
Vertex: _______
8. y = 3
­2
Vertex: _______
8
10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
Sketch the parabola by placing the vertex correctly and
correctly plotting the FIRST point.
9. y = ­
10. y = (x + 4)2 – 1
­2
Vertex: _______
11. y = –(x – 2)2 + 4
Vertex: _______
Vertex: _______
12. y = (x + 4)2
Vertex: _______
13. y = –(x + 3)2 – 1
Vertex: _______
14. y = (x – 3)2 + 2
Vertex: _______
15. y = (x – 0) 2 + 4
Vertex: _______
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10.1 graph absolute value and quadratic equations in vertex form 2016 2 ink.notebook
March 12, 2018
17. y = 3(x – 2)2 – 5
16. y = 2(x – 1)2 + 3
Vertex: _______
Vertex: _______
18. y = –2(x + 3)2 – 1
Vertex: _______
11) (2, 4)
Answers:
1) (-3, 4)
7) (0, 0)
3) (1, 5)
9) (-1, -2)
Answers:
13) (-3, -1)
5) (-2, -4)
15) (0, 4)
17) (2, -5)
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