2.8 Absolute Value Graphs
Warm up:
Quickly Graph y = 2 x + 1 − 4 using the information from yesterday.
X
y
-2
-3
-1
0
1
2
A.) Vertex: _____________
B.) Opens :______________
C.) Wider or more narrow: ________
The graph of y = a x − h + k has the following characteristics:
1.) The graph has a vertex ______________ and is symmetric to the line
____________.
How could you use your slope and symmetry to graph an absolute
value equation?
2.) The graph is ____________ shaped.
Opens up if _____________.
Opens down if ___________.
3.) The graph is wider than y = x if _________________.
4.) The graph is narrower than y = x if ______________.
Graph the following Equations.
1.) y = −2 x + 7 − 4
A.) h =
k=
Vertex: __________
B.) Symmetry :____________
C.) Slope: ___________.
D.) Opens :____________.
2.) y = 3 x − 1 − 2
A.) h =
k=
Vertex: __________
B.) Symmetry :____________
C.) Slope: ___________.
D.) Opens :____________.
3.) y =
2
x + 2 +1
3
A.) h =
k=
Vertex: __________
B.) Symmetry :____________
C.) Slope: ___________.
D.) Opens :____________.
Simply by looking at the graph of an absolute value equation what piece of
the equation y = a x − h + k is easily visible?
In order to write the equation of an absolute value equation in the form
y = a x − h + k you need the following from the graph:
1.) Vertex: __________________
2.) To solve for a:
a.) plug (h, k ) and one ordered pair ( x, y ) into the equation
y = a x − h + k and solve for a.
OR
b.) a is the same as your ______________.
1. Find vertex
2. Decide the direction your graph opens.
3. Use the _________ to find your a value.
Write the equation of the graphs shown below.
1.)
A.) Vertex: ______________
h=
k=
B.) a positive or negative _____
C.) Solve for a in the equation
by using a point or by using the
slope.
Equation of the Absolute Value Graph
y =ax−h +k
2.)
A.) Vertex: ______________
h=
k=
B.) a positive or negative _____
C.) Solve for a in the equation
by using a point or by using the
slope.
Equation of the Absolute Value Graph
y =ax−h +k
3.)
A.) Vertex: ______________
h=
k=
B.) a positive or negative _____
C.) Solve for a in the equation
by using a point or by using the
slope.
Equation of the Absolute Value Graph
y =ax−h +k
4.)
A.) Vertex: ______________
h=
k=
B.) a positive or negative _____
C.) Solve for a in the equation
by using a point or by using the
slope.
Equation of the Absolute Value Graph
y =ax−h +k
HW: pg. 126 #18-25, 34-39