Vocabulary: A quadratic function can be uniquely determined using three points with their x and y coordinates.

Example: Given points P₁(0,0), P₂(2,4), and P₃(3,9), we can solve for coefficients a, b, and c in f(x)=ax² + bx + c.

Highlight: The process involves creating a system of three equations and solving them simultaneously to find the function's coefficients.

Definition: The zeros of a quadratic function are the x-values where the function intersects the x-axis.

Example: For x² + 2x - 12 = 0, both graphical and algebraic solutions can be found using the quadratic formula or factoring.

Highlight: Multiple solution methods are presented, including the pq-formula and quadratic completion.

Example: A real-world application involving candy prices where f(m) = 0.016m represents the relationship between price and quantity.

Definition: Point verification involves checking if a given point satisfies the function equation.

Highlight: Understanding transformations of quadratic functions, including vertical and horizontal shifts.

Vocabulary: Streckfaktor (stretch factor) determines how the parabola is stretched or compressed.

Definition: Vertical shifts occur when adding or subtracting a constant (e), while horizontal shifts involve subtracting a constant (d) from x.

Highlight: For a>1, the parabola becomes narrower, while 0<a<1 results in a wider parabola compared to the normal parabola.

Definition: The vertex (Scheitelpunkt) represents either the minimum point for upward-opening parabolas or the maximum point for downward-opening parabolas.

Example: For the function f(x)=3x² + 6x + 7, the quadratic completion method transforms it into f(x)=3$x + 1$² + 4, revealing the vertex at (-1,4).

Highlight: The direction of the parabola's opening determines whether the vertex represents a minimum (a>0) or maximum (a<0).