1. Passport to advanced mathematics – lessons 5-7
Quadratic definitions and end behavior
Graphic solutions to quadratic-linear systems
Transformations
Composition of functions

2. Quadratic definitions and end behavior
Standard form ax2 + bx + c = 0
Vertex is at ( -b/2a , f(-b/2A))
The vertex is also called a turning point
Axis of symmetry passes through the vertex
Projectile motion: F(t) = -16(t – tm)2 + hm
Tm – time maximum is reached
Hm – maximum height

3. Graphic solutions to quadratic-linear systems
Algebraically: a solution to a system has to work in both equations
Graphically: a solution to a system is where the graphs intersect
Systems made from a quadratic and a linear equation can have no solution, one answer, or two answers

4. transformations
Everything outside of parentheses, exponents, radicals, or absolute value bars is a vertical transformation
Everything inside of parentheses, exponents, radicals, or absolute value bars is a horizontal transformation
These numbers need to be changed when they come out
Numbers in multiplication are stretches or shrinks
Greater than 1 – stretch, less than 1 – shrink
Numbers in addition or subtraction are shifts
Negative signs cause reflections

5. Composition of functions
Composition of functions means that the answer to the first step becomes the x for the last step
It’s like two problems in one
Compositions can be written two ways – always start at the back!
F(x) = p(q(x)) means plug x into the equation named q and get an answer, then plug that answer into the equation named P and get your final answer
F(x) = (p ∘ Q)(x) is another way to write the same problem