Page 2: Student's Solutions

This page shows the student's (Nicole Axyonov) solutions to the given problems.

For equation a (x² - 16 = 0), the student correctly identifies the solutions as x₁ = 4 and x₂ = -4.

For equation b (x² + 5x + 6 = 0), the student uses the quadratische Gleichung lösen Formel (quadratic formula) to find the solutions x₁ = -3 and x₂ = -2.

Definition: The quadratische Gleichung lösen Formel or quadratic formula is x = [-b ± √(b² - 4ac)] / (2a), where a, b, and c are the coefficients in the standard form of a quadratic equation (ax² + bx + c = 0).

For equation c (x² + 8x - 48 = 0), the student again applies the quadratic formula, finding the solutions x₁ = 4 and x₂ = -12.

The student chooses to solve word problem W2, setting up the equation x² + x = 240 and solving it to find x = 15.98 (approximately).

Example: The solution process for W2 involves:

1. Setting up the equation: x² + x = 240
2. Rearranging to standard form: x² + x - 240 = 0
3. Applying the quadratic formula or factoring to solve

Highlight: This page demonstrates the practical application of quadratische Gleichungen Übungen (quadratic equation exercises) and showcases various methods for solving different types of quadratic equations.

Page 1: Solving Quadratic Equations

This page presents a set of quadratic equations to be solved, along with some word problems applying quadratic equations to real-world scenarios.

The first task requires solving three quadratic equations:

a. x² - 16 = 0 b. x² + 5x + 6 = 0 c. x² + 8x - 48 = 0

Example: For equation a, x² - 16 = 0, the solution process involves isolating x²: x² = 16 Then, taking the square root of both sides: x = ±√16 x = ±4 Therefore, the solution set is {-4, 4}.

The second task offers a choice between two word problems:

W1: A problem involving the trajectory of a thrown football, modeled by the quadratic function y = -0.08x² + x + 2.

W2: A number puzzle where the square of a number plus the number itself equals 240.

Highlight: These word problems demonstrate practical applications of quadratische Gleichungen (quadratic equations) in physics and mathematics.

Vocabulary: Lösungsmenge refers to the solution set of an equation, which is the set of all values that satisfy the equation.