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Absolute Value and Quadratic Functions Unit 1
Transcript of Absolute Value and Quadratic Functions Unit 1
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:
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
Asymptotes: None Combination of Functions
G(f(x))= 2|x|^2+|6|+6 Addition:
|x| + 2x^2+x+6 Subtraction:
G(7)= 2(7)^2+(7)+6= 98+7+6=111
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.