Quadratic Equations

1
Quadratic Equations
A term like x2 is called a square in algebra
because it is the area of a square with side x
The adjective quadratic comes from the Latin
word quadratum for square.
So a quadratic equation is one in which the
highest index number of a term with x in is x2
Examples of quadratic equations
y x2
y x2 1
y x2 3x - 10
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Quadratic Equations
These equations can be drawn as graphs in the
same way that we know how to draw straight line
graphs.
By substituting the given values for x calculate
the y value for the following equation
y x2
x -3 -2 -1 0 1 2 3
y              
9
4
1
1
9
0
4
This generates coordinates to plot on a graph
(-3,9)
(1, 1)
Notice how the y values are symmetrical
(2, 4)
(-2,4)
(-1, 1)
(3, 9)
(0, 0)
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Plotting these points
Quadratic Equations
(-3,9)
(1, 1)
(2, 4)
(-2,4)
(-1, 1)
(3, 9)
x
x
(0, 0)
What is the name of this shape?
x
x
Parabola
x
x
Why is it this shape?
x
because x2 is always positive, even when x itself
is negative
The lowest point is called the minimum
and the value of y increases at a much faster
rate than x
4
Quadratic Equations
Draw the graph for the following quadratic
function
y x2 1
x
x
Complete the table
x -3 -1 0 1 3
y          
10
2
1
10
2
x
x
Draw the graph
x
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Quadratic Equations
Drawing graphs of more complex quadratic
functions we need bigger tables with more data in
order to be able to draw the graphs accurately
Draw the graph of this function
y x2 - 3x - 2
x -4 -3 -2 -1 0 1 2 3 4
x2                  
-3x                  
-2                  
y                  
16 9 4 1 0 1 4 9 16
12 9 6 3 0 -3 -6 -9 -12
Now add all the values together to find y
-2 -2 -2 -2 -2 -2 -2 -2 -2
-2
-4
-4
16
8
2
-2
26
2
6
Quadratic Equations
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Quadratic Equations
Draw the graph of this function
y x2 3
x -4 -3 -2 -1 0 1 2 3 4
x2                  
3                  
                 
y                  
3 3 3 3 3 3 3 3 3
19 12 7 4 3 4 7 12 19
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Quadratic Equations
Draw the graph of this function
y x2 2x 1
x -4 -3 -2 -1 0 1 2 3 4
x2
2x
1
y            
16 9 4 1 0 1 4 9 16
-8 -6 -4 -2 0 2 4 6 8
11 11 1 11 11
9 4 1 0 1 4 9 16 25
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Quadratic Equations
Draw the graph of this function
y 2x2 x 3
x -4 -3 -2 -1 0 1 2 3 4
2x2                  
-x                  
3                  
y                  
32 18 8 2 0 2 8 18 32
43 21 0 -1 -2 -3 -4
33 33 33333
37 2413 6 3 4 9 18 31
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Quadratic Equations
Worksheet 1
Draw the graph of this function
y x2 3
x -4 -3 -2 -1 0 1 2 3 4
x2                  
3                  
                 
y                  
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Quadratic Equations
Worksheet 2
Draw the graph of this function
y x2 2x 1
x -4 -3 -2 -1 0 1 2 3 4
x2                  
2x                  
1                  
y                  
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Quadratic Equations
Worksheet 3
Draw the graph of this function
y 2x2 x 3
x -4 -3 -2 -1 0 1 2 3 4
                 
                 
                 
y