1. Quadratic Equations
1.1. Solve Quadratic Equations
1.1.1. Find Statement with 2 solutions/roots
1.1.1.1. Factoring
1.1.1.2. Completing the squares
1.1.1.3. Quadratic Formula
1.1.1.3.1. Complex Number System
1.1.1.3.2. Used to find zeros of a quadratic relation
1.1.1.4. Discriminant and Nature of Roots
1.1.1.4.1. *correction to the image: b^2-4ac > 0 has 2 different real roots b^2-4ac > 0 (if not a perfect square, like 2 or 3) has 2 real irrational roots b^2-4ac = 0 has 2 equal real roots b^2-4ac < 0 has 2 different complex roots
1.2. Solving Problems involving Quadratic Equations
1.2.1. 1) Build a Model 2) Let Statements 3) Clear Fractions 4) Simplify 5) Solve by factoring or quadratic formula
1.3. Maxima and Minima
1.3.1. 1) Create Equation of Constraint 2) Isolate for Variable 3) Simplify 4) Complete Squares 5) Identify vertex
1.3.2. To Optimize
1.3.3. Minimum point of vertex: a>0 Maximum point of vertex: a<0
2. Quadratic Expressions
2.1. Multiplying Polynomials and Binomials
2.1.1. Polynomials
2.1.2. Binomials
2.2. Special Products
2.2.1. Perfect Square Trinomial
2.2.2. Difference of Squares
2.3. Common Factors
2.3.1. Group Factoring
2.3.1.1. May use multiple techniques
2.3.2. Greatest Common Factor to find two or more terms
2.3.3. Difference of Squares to find two terms
2.4. Factor form ax^2 + bx + c
2.4.1. Inspection
2.4.2. Decomposition
3. Quadratic Relations
3.1. Parabola
3.2. Finite Differences
3.2.1. Second Difference means that the equation is quadratic
3.3. Standard Form
3.3.1. a CANNOT equal 0 a, b, c are real numbers
3.4. Factored Form
3.4.1. Expand to get standard form
3.4.2. r and s represent the zeros
3.5. Non-linear Relations
3.5.1. Curve of Best Fit
3.6. Transformations
3.6.1. Reflections
3.6.1.1. a<0
3.6.2. Vertical Stretch
3.6.2.1. a>1 or a<-1
3.6.3. Vertical Compression
3.6.3.1. 0<a<1 or -1<a<0
3.6.4. Translations
3.6.4.1. Units Right: h>0
3.6.4.2. Units Left: h<0
3.6.4.3. Units Up: b>0
3.6.4.4. Units Down: b<0
3.7. Vertex Form
3.7.1. Complete Squares from Standard form
3.7.2. Opens up: a>0 Opens Down: a<0 X Values/Domain: D{x|xεR} Y Values/Range: if a>0, then y ≥ b if a<0, then y ≤ b
3.8. Zeros
3.8.1. b^2-4ac > 0 has 2 zeros
3.8.2. b^2-4ac = 0 has 1 zero
3.8.3. b^2-4ac < 0 has no zeros