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Quadratic Functions
� General form
� Other forms : 1 .
2 y � ax �bx � c , where a � 0 :
a �
0
|
The graph opens upward |
a �
0
|
The graph opens downward |
c |
y -intercept |
b h
��
2a
|
x -coordinate of the vertex |
2 k
� ah
�bh
� c
|
y -coordinate of the vertex
Extreme value of y
|
x
2 y a( x h) k
� h Equation of the axis of symmetry
� � � : Vertex form 2 . y � a( x � p)( x � q)
: Factored form with x -intercepts p and q b p � q
� h � � � 2a
2
� The x -intercepts of the quadratic function corresponding quadratic equation
2 ax bx c
2 y � ax �bx � c are the roots of the � � � 0
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Exponential and Logarithmic Functions
x
� y� a : Exponential function , where a � 1
� y� log a x: Logarithmic function , where a � 0
� log log10 y � x � x : Common Logarithmic function
� y �ln x � log e x : Natural Logarithmic function , where e � 2.71828 ... is an
exponential number www . seprodstore . com
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