Quadratic Equations

A quadratic equation is a second-degree polynomial equation in a single variable x. It has the form:

ax² + bx + c = 0

Where a, b, and c are constants with a ≠ 0, and x represents an unknown variable.

Standard Form

The standard form of a quadratic equation is given by:

ax² + bx + c = 0

Quadratic Formula

The solutions for the quadratic equation in the form ax² + bx + c = 0 can be found using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Vertex Form

The vertex form of a quadratic equation is given by:

y = a(x - h)² + k

Where (h, k) represents the vertex of the parabola.

Study Guide

1. Understand the standard form of quadratic equations.
2. Learn how to solve quadratic equations using the quadratic formula.
3. Practice completing the square to convert quadratic equations to vertex form.
4. Understand the graphical representation of quadratic equations as parabolas.
5. Practice solving word problems involving quadratic equations.

Remember to practice solving various types of quadratic equations to strengthen your understanding of the topic.

Good luck with your studies!