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Absolute Value and Quadratic Functions Unit 1

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by

Paige Garrett

on 29 January 2013

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Transcript of Absolute Value and Quadratic Functions Unit 1

Madeline Hamiter, Paige Garrett Unit 1 Project
Quadratic Vs. Absolute Value The similarities and differences in the different equations,
What the 2 functions look like for examples,
The basic properties of the functions,
and how they relate to arithmetic. What we will cover.. Basic Quadratic Functions:
ax^2+bx+c, when a is not equal to 0.
Domain: All Real Numbers
Range: Find the Y value of Max/Min if max is the highest point on the parabola then Y is ≥All Real Numbers. If Min is at the bottom of parabola then Y is ≤ All Real numbers.
Symmetries: Reflectional at -b/2a.
Asymptotes: None Basic Absolute Value Functions:
Example: F(x)=|X|
Absolute Value Portray equations that are absolutely a certain value. Everything in “| |” are absolutely positive and everything out of the “| |” is going to be the same sign as it usually is.
Domain: All real numbers
Range: all real numbers ≥ 0
Symmetries: Reflectional
Asymptotes: None Combination of Functions
F(x)= |x|
G(x)=2x^2+x+6

F(g(x))=|2x^2+x+6|
G(f(x))= 2|x|^2+|6|+6 Addition:
|x| + 2x^2+x+6 Subtraction:
|x|-2x^2-x-6 Multiplication:
|x|*(2x^2+x+6) Division:
|x|/(2x^2+x+6) Example:
[F÷G](5)
F(5)=|5|= 5
G(5)= 2(5)^2+(5)+6=50+5+6=61
5/61
.08 Example:
[F*G](7)
F(7)=|7|= 7
G(7)= 2(7)^2+(7)+6= 98+7+6=111
7*111=777 Example:
[F-G](-2)
F(-2)=|-2|= 2
G(-2)= 2(-2)2+(-2)+6=8+-2+6=12
2-12=-10 Example:
[F+G](-2)
F(-2)=|-2|= 2
G(-2)= 2(-2)^2+(-2)+6=8+-2+6=12
2+12= 14 The composition of a absolute value function and a quadratic function is a cross between a quadratic graph and an absolute value graph because the graph of the combined functions is in a similar shape of absolute value (a straight V) but it is curved like a quadratic. They are not commutative.
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