Step-by-Step Solutions

This page provides detailed solutions for converting the given quadratic functions from faktorisierte Form to Normalform. Each solution follows a consistent approach:

1. Expand the factored form using the distributive property
2. Combine like terms
3. Present the final result in standard form (ax² + bx + c)

Example: For f(x) = (x-3)(x-5):

1. Expand: x² - 5x - 3x + 15
2. Combine like terms: x² - 8x + 15
3. Final result in Normalform: f(x) = x² - 8x + 15

Highlight: The solutions demonstrate that the coefficient of x² is always 1 in these examples, which is a characteristic of faktorisierte Form when the leading coefficient is not explicitly stated.

Vocabulary: Ausmultiplizieren is the German term used throughout the page, which means "to multiply out" or "to expand".

The page covers all 22 problems presented on the previous page, providing a comprehensive set of worked examples for students to study and understand the process of converting from faktorisierte Form to Normalform.

Highlight: These exercises include various combinations of positive and negative factors, helping students recognize patterns and develop proficiency in handling different types of quadratic expressions.

By working through these examples, students can gain a solid understanding of the relationship between the faktorisierte Form and Normalform of quadratische Funktionen (quadratic functions), which is essential for further study of polynomial functions and algebraic manipulation.