Quadratic Graph Drawing'

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Quadratic Graph Drawing.
y 4x2 4x 3
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Quadratic Graph Structure.
Consider the typical quadratic graph shape below
To draw a quadratic graph you must be able to
calculate all the points numbered on the diagram
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The significance of each point and the starting
point to finding the point are given below

• Point of intersection with the y axis.

Graph cuts y axis when x 0
(2) Point of intersection with x axis.
Graph cuts x axis when y0
These are the roots of the equation.
(3) Turning point of graph.
Turning point x coordinate is the midpoint of the
roots.
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Graph Of Type y x2 a2
Sketch the graph of y x 2 - 9
(1) Find the y axis intercept.
Graph cuts y axis when x 0
Point ( 0, -9 ) is on the graph.
(2) Find the x axis intercept.
Graph cuts x axis when y 0.
(x 3 ) (x 3 ) 0
The points (3,0) and (-3,0) are on the graph.
x 3
x - 3
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(3) Turning point of graph.
Y x2 - 9
Turning point x coordinate is the midpoint of the
roots.
From the symmetry of the graph we can see that
this point must be (0,-9).
Now sketch the graph.
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Example 2
Sketch the graph of y x 2 - 25
(1) Find the y axis intercept.
Graph cuts y axis when x 0
Point ( 0, -25 ) is on the graph.
(2) Find the x axis intercept.
Graph cuts x axis when y 0.
(x 5 ) (x 5 ) 0
The points (5,0) and (-5,0) are on the graph.
x 5
x - 5
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(3) Turning point of graph.
Y x2 - 25
Turning point x coordinate is the midpoint of the
roots.
From the symmetry of the graph we can see that
this point must be (0,-25).
Now sketch the graph.
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What Goes In The Box ? 1
Sketch the graph of the following functions
(1) y x2 - 4
(2) y x2 - 36
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Graphs Of Type y ax2 bx c
Sketch the graph of y x 2 2x 24
(1) Find the y axis intercept.
Graph cuts y axis when x 0
The point (0,-24) is on the graph.
(2) Find the x axis intercept.
Graph cuts x axis when y 0.
(x 6) (x 4) 0
The points (-6,0) and (4,0) are on the graph.
x - 6
x 4
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(3) Turning point of graph.
y x 2 2x 24
Turning point x coordinate is the midpoint of the
roots.
Substitute x -1 into the equation y x 2
2x 24 to find the y coordinate.
y (-1)2 (2 x 1) 24 - 25
The point (-1,-25) is the minimum turning point.
Now sketch the graph.
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Example 2.
Sketch the graph of y 4x2 4x 3
(1) Find the y axis intercept.
Graph cuts y axis when x 0
Y 3
The point (0,-3) is on the graph.
(2) Find the x axis intercept.
Graph cuts x axis when y 0.
( 2x 1 )( 2x 3 ) 0
The points (-1/2,0) and (3/2,0) are on the graph.
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(3) Turning point of graph.
y 4x2 4x 3
Turning point x coordinate is the midpoint of the
roots.
Substitute x ½ into the equation y 4x2
4x 3 to find the y coordinate.
y - 4
Minimum turning point (1/2, -4)
Now sketch the graph.
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What Goes In The Box? 2
Sketch the graphs of the equations given below
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Graph Of Type y a2 x2
Sketch the graph of y 25 x2
y 25 x2
(1) Find the y axis intercept.
Graph cuts y axis when x 0
y 25
The point ( 0,25 ) is on the graph
(2) Find the x axis intercept.
5
-5
Graph cuts x axis when y 0.
25 x2 0
( 5 x ) ( 5 x ) 0
The effect of the negative x2 is to make the
graph A shaped.
x 5
x - 5
The points (0,5 and (0,-5) are on the graph.
Now sketch the graph.
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Example 2
Sketch the graph of y x2 x 6
(1) Find the y axis intercept.
Graph cuts y axis when x 0
y 6
The point ( 0,6 ) is on the graph
(2) Find the x axis intercept.
Graph cuts x axis when y 0.
x2 x 6 0
Divide throughout by -1
x2 - x - 6 0
( x 3) ( x 2 ) 0
The points ( 3, 0 ) and ( -2 , 0 ) are on the
graph.
x 3
x - 2
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(3) Turning point of graph.
y - x2 x 6
Turning point x coordinate is the midpoint of the
roots.
Substitute x ½ into the equation y - x2
x 6 to find the y coordinate.
The maximum turning point is ( 0.5, 6.25 )
Now sketch the graph.
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What Goes In The Box ? 3
Sketch graphs of the quadratic equations below