The Graphs of Quadratic Equations

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The Graphs of Quadratic Equations
Saturday, 21 November 2009
A quadratic equation is an equation that has a x2
value. All of these are quadratics y
x2 y x2 2 y x2 x 4 y
x2 2x 3
So quadratic means that there must be a x2 in
what ever y equals
2
If you were asked to draw the graph of y x2
2, follow these steps
Draw a chart putting in the x values from 4 to 4
The exam writer will probably do this for you
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If you were asked to draw the graph of y x2
2, follow these steps
Calculate x2 and put these values into the table.
Notice that all of these are positive
The values are always positive because a minus
time a minus is a plus -3 X 3 9 etc.
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If you were asked to draw the graph of y x2
2, follow these steps
Add the 2 onto the x2 and put these values into
the table.
5
If you were asked to draw the graph of y x2
2, follow these steps
You have done all that the equation asks so you
will have the y value.
All you need to do now is to plot the x number
against the y number.
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If you were asked to draw the graph of y x2 x
4, follow these steps
Draw a chart putting in the x values from 4 to 4
The exam writer will probably do this for you
8
If you were asked to draw the graph of y x2 x
4, follow these steps
Calculate x2 and put these values into the table.
Notice that all of these are positive
The values are always positive because a minus
time a minus is a plus -3 X 3 9 etc.
9
If you were asked to draw the graph of y x2 x
4, follow these steps
Add the x onto the x2 and put these values into
the table.
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If you were asked to draw the graph of y x2 x
4, follow these steps
Subtract 4 from these values to obtain
x2 x 4.
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If you were asked to draw the graph of y x2 x
4, follow these steps
You have done all the equation asks so you must
have the y value.
All you need to do now is to plot the x number
against the y number
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If you were asked to draw the graph of y 8 - x2
follow these steps
Start a table with x values
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If you were asked to draw the graph of y 8 - x2
follow these steps
Find the value of x2
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If you were asked to draw the graph of y 8 - x2
follow these steps
Find the value of 8 x2
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If you were asked to draw the graph of y 8 - x2
follow these steps
3)You have done all the equation asks so you must
have the y value.
All you need to do now is to plot the x number
against the y number
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Solve by factorising and completing the square 0
x2 2x - 8
Complete the table and draw the graph of the
above quadratic and explain connections between
the graph, factorising and completing the square
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x2 2x 8 0 (x 4)(x - 2) 0 x -4 and 2
x2 2x 8 0 (x 1)2 8 12 0 (x 1)2
9 0