To draw the graph of the form:
y = a·|bx + c| + d
This is a graph shaped like this "⋁" or like this "⋀".
1. Find the vertex (The sharp point of the graph)
A. Set bx + c = 0 and solve for x. This is the x-coordinate of the
vertex.
B. The y-coordinate of the vertex is d.
C. Plot this point.
2. Find a point on the left of the vertex
A. Select a value of x less than the x coordinate of the vertex
for the x-ccordinate of a second point on the graph.
B. Substitute this value into the equation to find the corresponding
y-coordinate for that point.
C. Plot that point.
3. Find a point on the right of the vertex
A. Select a value of x greater than the x coordinate of the vertex
for the x-ccordinate of a third point on the graph.
B. Substitute this value into the equation to find the corresponding
y-coordinate for that point.
C. Plot that point.
4. Draw a graph through those three points shaped like this "⋁" or like
this "⋀", with the vertex at the sharp point.
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Let's go through your problem with those rules.
y = |3x - 6| + 1
Compare to
y = a·|bx + c| + d
a=1, b=3, c=-6, d=1
1. Find the vertex (The sharp point of the graph)
A. Set bx + c = 0 and solve for x.
3x - 6 = 0
3x = 6
x = 2
This is the x-coordinate of the vertex.
B. The y-coordinate of the vertex is d=1.
C. Plot this point, which is (2,1)
2. Find a point on the left of the vertex
A. Select a value of x less than the x coordinate of the vertex
for the x-ccordinate of a second point on the graph.
Let's select 1 which is less than 2
B. Substitute this value into the equation to find the corresponding
y-coordinate for that point.
y = |3x - 6| + 1
y = |3(1) - 6| + 1
y = |3 - 6| + 1
y = |-3| + 1
y = 3 + 1
y = 4, so the second point is (1,4)
C. Plot that point.
3. Find a point on the right of the vertex
A. Select a value of x greater than the x coordinate of the vertex
for the x-ccordinate of a third point on the graph.
Let's select 3 which is greater than 2
B. Substitute this value into the equation to find the corresponding
y-coordinate for that point.
y = |3x - 6| + 1
y = |3(3) - 6| + 1
y = |9 - 6| + 1
y = |3| + 1
y = 3 + 1
y = 4, so the third point is (3,4)
C. Plot that point.
4. Draw a graph through those three points shaped like this "⋁" or like
this "⋀", with the vertex at the sharp point.
In this case it is shaped like this "⋁", so we draw in the graph:
Edwin
