Page 1: Converting Between Function Forms

This page introduces the fundamental concepts of converting quadratic functions between different forms, particularly focusing on the postać iloczynowa funkcji kwadratowej and its transformations.

Definition: The factored form of a quadratic function is expressed as f(x) = a(x-x₁)(x-x₂), where x₁ and x₂ are zeros of the function.

Highlight: To convert from factored to general form, multiply out the brackets following the distributive property.

Example: Converting from factored to general form: f(x) = a(x²-x₂x-x₁x+x₁x₂) → f(x) = ax²-a(x₁+x₂)x+ax₁x₂

Vocabulary: The vertex coordinates (p,q) are essential for the canonical form, where p is the x-coordinate halfway between the zeros, and q is the y-coordinate calculated by evaluating the function at p.