Linear Functions
Linear Equations
Standard : ax + by = c
Slope-Intercept : y = mx + b
Point-Slope : y - y1 = m ( x - x1)
Vertical : x = #
Horizontal : y = #
Quadratic Functions
Methods of Solving + Possible Outcomes
Elimination
Substitution
Graphing
Matrices
Intersection (1 Solution)
Parallel (0 Solutions)
Same Line (Infinite Solutions)
Methods of Solving + Discriminant
Quadratic Equations
Standard : y = ax^2 + bx + c
Vertex : y = a ( x - h )^2 + k
Factoring
Quadratic Formula
Graphing
Completing the Square
If Discriminant Less than 0, then there are 0 Real Solutions
If Discriminant Equals 0, then there is 1 Real Solution
If Discriminant Greater than 0, then there are 2 Real Solutions
Example : y = 2x^2 + 7x + 6
Example : y = - 2( x - 3)^2 + 7
Example : 3x + 4y = 11
Example : 6 - 4 = 3 (7 - 2)
Example : y = - 5x + 3
Example : x = 4
Example : y = -16
Completing the Square
- Simplify by Taking Square Root and Solving
- Complete Square by Adding (b/2)^2 to Both Sides
- Move Constant
- Divide by "a" term