Introduction

Quadratic functions are essential components of algebra with applications in various fields, represented by a polynomial of degree 2.

Key Concepts

This section outlines the essential concepts related to quadratic functions, including their forms, graphs, and methods for solving equations.

Standard Form Of A Quadratic Function

This section introduces quadratic functions, detailing their standard form and graphical properties.

Graph Of A Quadratic Function

This section covers the graphical representation of quadratic functions, discussing key features such as the vertex, axis of symmetry, and types of intercepts.

Vertex (Turning Point)

The vertex represents the turning point of a quadratic function, indicating its maximum or minimum value.

Axis Of Symmetry

The axis of symmetry in a quadratic function is a crucial line that divides the parabola into two identical halves and passes through the vertex.

Y-Intercept

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

X-Intercepts (Roots Or Zeros)

This section covers x-intercepts, also known as roots or zeros, of quadratic functions and various methods to find them.

Methods Of Solving Quadratic Equations

This section details the various methods for solving quadratic equations, including factoring, completing the square, and using the quadratic formula.

Factoring

Factoring is a method used to solve quadratic equations by expressing them as products of binomials.

Completing The Square

In this section, we learn how to complete the square, a technique used to solve quadratic equations and transform quadratic functions into vertex form.

Quadratic Formula

The quadratic formula is a key method for solving quadratic equations and understanding the nature of their roots.

Worked Examples

This section presents worked examples that illustrate the application of methods for solving quadratic equations.

Example 1: Factoring

Example 2: Completing The Square

Example 3: Using The Quadratic Formula

Practice Questions

This section presents practice questions aimed at reinforcing understanding of quadratic functions and their applications.

Real-Life Applications

Quadratic functions play a vital role in various real-world contexts, including physics, economics, and engineering.

Chapter Summary

This section summarizes the key aspects of quadratic functions, including their form, graphical representation, and methods for solving related equations.