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Quadratic Equations

Master quadratic equations with interactive lessons and practice problems! Designed for students like you!

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Quadratic Equations

Study Guide

Key Definition

A quadratic equation is of the form $ax^2 + bx + c = 0$ where $a \neq 0$.

Important Notes

A quadratic equation graph is a parabola.
The solutions are found where the parabola intersects the x-axis.
Use $ax^2 + bx + c = 0$ for standard form.
The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
Factoring can be used when the equation is factorable.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$\sqrt{x}$ represents the square root of x

Remember to use proper notation when solving problems

Why It Works

Quadratic equations model many real-world scenarios with parabolic paths, allowing predictions and solutions with formulas.

Remember

The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ provides solutions to any quadratic equation.

Quick Reference

Standard Form:$ax^2 + bx + c = 0$

Understanding Quadratic Equations

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $x^2 + bx + c = 0$ as the basic formula; note this is the case $a = 1$ of the general form $ax^2 + bx + c = 0$ with $a \neq 0$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve $x^2 - 5x + 6 = 0$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A skateboarder's height (in meters) after x seconds is modeled by $h(x) = -x^2 + 6x + 8$. Find the maximum height (the peak value of h(x)).

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine the number of real solutions for $3x^2 - 6x + 2 = 0$ using the discriminant.

Challenge Quiz

Single Choice Quiz

Advanced

Solve $2x^2 - 4x + 2 = 0$ using the quadratic formula.

Recap

Watch & Learn

Review key concepts and takeaways