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

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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

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Completing the Square

  1. Simplify by Taking Square Root and Solving
  1. Complete Square by Adding (b/2)^2 to Both Sides
  1. Move Constant
  1. Divide by "a" term

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