8th Grade Math

Quadratic Formula

Solve equations in the form ax² + bx + c = 0 by plugging values into the quadratic formula and simplifying step by step.

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What It Is

The Quadratic Formula

The quadratic formula is a shortcut for solving any quadratic equation written as ax² + bx + c = 0.

It gives you the value or values of x without guessing factors first.

x = -b ± √(b² - 4ac)2a

You use it when an equation has an x² term and you want to find the roots, also called the solutions.

In this module, the generated problems have real-number answers so you can practice the process clearly.

How To Solve It

Quadratic Formula Steps

Use these steps every time you generate a new equation.

1. Identify a, b, and c

Match each number in the equation ax² + bx + c = 0.

Example:

In x² - 5x + 6 = 0, a = 1, b = -5, and c = 6.

2. Plug into the formula

Substitute the values into x = (-b ± √(b² - 4ac)) / 2a.

Example:

x = -(-5) ± √((-5)² - 4(1)(6)) / 2(1)

3. Simplify the discriminant

The part under the square root is called the discriminant.

Example:

b² - 4ac = 25 - 24 = 1

So the square root part becomes √1.

4. Solve both answers

Because of the ± sign, you usually get two solutions.

Example:

x = (5 ± 1) / 2

So the answers are x = 3 and x = 2.

Current Problem Generate a quadratic equation to begin.

Professor Foxwell will give you an equation with two real-number solutions.

Helpful Math Words

Quadratic Formula Vocabulary

These words can help you understand what each part of the equation means.

Quadratic Equation

An equation with an x² term, like x² - 5x + 6 = 0.

Coefficient

The number attached to a variable. In -5x, the coefficient is -5.

Constant

A number with no variable. In x² - 5x + 6 = 0, the constant is 6.

Discriminant

The part inside the square root: b² - 4ac. It tells you what kind of answers you will get.

Square Root

A number that multiplies by itself to make another number, like √9 = 3.

Solution / Root

A value of x that makes the equation true.

Parabola

The U-shaped graph of a quadratic equation.

Real Number Solution

An answer you can place on the number line, like 2 or -3.