Page 2: Completing the Square Method

This page focuses on the technique of completing the square and provides a detailed example of solving a quadratic equation using this method. The process is demonstrated through a step-by-step solution of the equation x² + 4x - 6 = 0.

Definition: Completing the square is a method used to solve quadratic equations by creating a perfect square trinomial.

Example: For x² + 4x - 6 = 0, the solution process involves:

1. Moving the constant term to the right side
2. Adding the square of half the coefficient of x
3. Factoring the perfect square trinomial
4. Taking the square root of both sides
5. Solving for x

Highlight: The method results in two solutions: x = -2 - √10 ≈ -5.16 and x = -2 + √10 ≈ 1.16

Vocabulary: Perfect square trinomial is a quadratic expression that can be factored as the square of a binomial.

Page 1: Factoring and Quadratic Equations

This page introduces fundamental concepts of factoring quadratic equations and demonstrates various solution methods. The content progresses from basic factoring to more complex problems involving different coefficients.

Definition: Factoring is the process of breaking down a quadratic expression into the product of its factors.

Example: The equation k + 1$$k - 5 = 0 demonstrates basic factoring where solutions are found when either factor equals zero.

Highlight: When factoring quadratic equations with leading coefficient 1, the process is straightforward and involves finding two numbers that multiply to give c and add to give b in the standard form ax² + bx + c.

Vocabulary: Leading coefficient refers to the coefficient of the highest degree term (x²) in a quadratic equation.

The page also covers the method of factoring quadratic equations where the leading coefficient is not 1, following these steps:

1. Multiply a and c
2. Split the middle term
3. Find the Greatest Common Factor (GCF)
4. Group terms and factor