# Quadratic Equations and Function Evaluation

This section of the AP Calculus AB Summer Packet focuses on quadratic equations and function evaluation, two critical areas that form the foundation for more advanced calculus concepts.

The first part of this section (problems 17-22) requires students to solve quadratic equations by factoring. These problems include:

- Standard quadratic equations (ax² + bx + c = 0)
- Perfect square trinomials
- Difference of squares

**Example**: One problem asks students to solve x² - 6x + 9 = 0, which is a perfect square trinomial.

**Highlight**: The packet includes a video demonstration on factoring, emphasizing the importance of this skill for solving quadratic equations.

The second part of this section (problems 23-27) focuses on function evaluation. Students are given two functions, f(x) = 5 - 1/x and g(x) = x² + 3x, and are asked to evaluate these functions for various inputs and combinations.

**Example**: One problem asks students to calculate f(1) + g(0), requiring them to evaluate each function separately and then combine the results.

The final part of this section (problems 28-35) introduces the concept of composite functions. Students are given three functions, f(x) = x² - 1, g(x) = 3x, and h(x) = 5x, and are asked to find various composite functions.

**Vocabulary**: A **composite function** is a function that is composed of two or more functions, where the output of one function becomes the input of another.

These exercises help students develop their skills in:

- Solving quadratic equations
- Evaluating functions for specific inputs
- Working with composite functions

These skills are crucial for success in AP Calculus AB, as they form the basis for understanding more complex calculus concepts such as limits, derivatives, and integrals. By mastering these fundamental skills, students will be better prepared to tackle the challenges of the AP Calculus AB curriculum.