highschool/Grade 10/Math/MPM2DZ/Unit 3: Quadratic Functions.md

Unit 3: Quadratic Functions

Definitions

• Linear relation: A relation with a constant rate of change
• Non-linear relation: A relation with a variable rate of change
• Degree of a polynomial: Highest exponent that appears in any term of a polynomial
• a-value: Step property
• Axis of symmetry: Vertical symmetrical line through a parabola, also x-value for vertex
• Zeroes: x-intercepts of parabola
• Vertex: Maximum or minimum value on a parabola
• Optimal value: y-value for vertex
• Domain: List of all valid x-values for relation, expressed as \(`D = {num, num2, num3}`\) or as a relation such as \(`D = {x E R, x != 0, x < 50`\)
• Range: List of all valid y-values for relation, expressed as \(`R = {num, num2, num3}`\) or as a relation such as \(`D = {y E R, y != 0, y < 50`\)
• Relation: Set of ordered pairs of numbers
• Function: A relation in which no y-coordinates share an x-coordinate (e.g., circles are not functions)

Parabolas

Transformations

Forms of Quadratic Functions

Standard Form

Vertex Form

Factored Form

Quadratic Inequalities