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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# Absolute Value and Quadratic Functions Unit 1

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