Page 1: Introduction to Quadratic Functions

This page introduces the concept of funkcja kwadratowa and its basic properties.

Key points:

• A quadratic function is defined as y=ax^2+bx+c, where a≠0
• The domain of a quadratic function is all real numbers
• The graph of a quadratic function is a parabola
• The parabola's orientation depends on the sign of 'a'
• The y-intercept of the parabola is at point (0,c)

Definition: A funkcja kwadratowa is a function that can be expressed in the form y=ax^2+bx+c, where a, b, and c are real numbers and a≠0.

Highlight: The shape and orientation of the parabola are determined by the coefficient 'a'. When a>0, the parabola opens upward, and when a<0, it opens downward.

Example: In the function y=x^2-2√2x^2-8, we can identify a=1-2√2, b=0, and c=-8.

The page also introduces the canonical form of a quadratic function, y=a(x-p)^2+q, where (p,q) represents the vertex of the parabola.

Page 3: Applications and Inverse Proportionality

This page discusses applications of quadratic functions and introduces the concept of inverse proportionality.

Key points:

• Inverse proportionality is defined by the equation y=a/x, where x≠0 and a≠0
• The graph of an inverse proportion is a hyperbola
• Inverse proportions have specific properties regarding their domain and range

Definition: Proporcjonalność odwrotna (inverse proportionality) is a relationship defined by the equation y=a/x, where x≠0 and a≠0. The constant 'a' is called the coefficient of inverse proportionality.

Highlight: The graph of an inverse proportion is a hyperbola, which has two separate branches in different quadrants of the coordinate plane.

The page also covers properties of inverse proportions:

• If a>0, the graph lies in the first and third quadrants
• If a<0, the graph lies in the second and fourth quadrants
• The domain and range exclude zero

Example: In the equation xy=(x-2)(y+3), we can determine if it represents an inverse proportion by solving for x and y.

This page emphasizes the practical applications of quadratic functions and inverse proportionality in real-world scenarios.