Math 121
Section 1.2
Graphing Equations
Sketching Graphs
Examples
1) 
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-2 |
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Plot the following values (-2,4),(-1,1),(0,0),(1,1),(2,4) from the table will give the following graph.
2) Graph 
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Plot the values from the table will result in the following graph
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Plot the values from the table will give you a v-shaped graph
Again, use a table of values to make a graph of the equation
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9 |
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Resulting Graph
The graph of 
Horizontal and
Vertical Translations (Shifts)
Horizontal Translation: An operation that moves the graph of an equation to the left or right while at the same time preserves the shape of the graph.
Vertical Translation: An operation that moves the graph of an equation to the left or right while at the same time preserves the shape of the graph.
Example of a Vertical
Translation
1) 
Since the -2 lies outside the 
term, the value -2 indicates a vertical translation of 2
units. The negative sign in value of -2
indicates that the translation will move the graph of down two units as shown below:
The graph of
The graph of shifted down to units
Example of a Horizontal Translation
In this example, the -2 inside the parentheses indicates that there is a horizontal translation of two units to the right. A negative sign inside the parentheses will always result in a shift to the right.
The original graph of 
The graph ofafter a horizontal translation of 2 units to the right
The graph of 
The graph of
The graph of
is the inverted graph of. The negative sign in
front of the
term simple turns the graph of upside down.
Circles
Given a circle with center (h,k) and radius r, use the distance formula to find the equation of the circle
Thus, the equation a circle in standard form with radius r
and center (h,k) is given by 
General Form of an Equation of a circle
Examples
1) Write the equation of a circle in standard form given the radius is 5 and the center is (0,0).
2) Write the equation of a circle in standard form given the radius is 4 and the center is
(-4,5).
3) Find the center and radius of a circle with the given equation
Note: To complete the
square for the 4x term take half of 4 which is 2 and find 
To complete the
square for the 6y term take half of 6 which is 3 and find 
4) Find the center and radius of a circle with the given equation
Note: To complete the
square for the -8x term take half of 8 which is 4 and find 
To complete the
square for the -2y term take half of 2 which is and find 
3) Find the center and radius of a circle with the given equation
