Quadratic Formula Calculator

What Is a Quadratic Formula Calculator?

A quadratic formula calculator is an online algebra calculator that helps solve quadratic equations using the formula x = (-b ± √(b² - 4ac)) / 2a. It is useful for algebra homework, high school math, college algebra, SAT math practice, ACT math practice, and checking answers.

This quadratic calculator with steps can work as a quadratic formula solver, quadratic roots calculator, discriminant calculator, and ax2 bx c calculator for equations written in standard form.

How to Use This Quadratic Formula Calculator

1. Enter the coefficient a.
2. Enter the coefficient b.
3. Enter the coefficient c.
4. Click Calculate.
5. Review the roots, discriminant, and step-by-step work.

You can also use the example buttons to quickly test common equations and learn how each solution is created.

Quadratic Equation Standard Form

A quadratic equation is usually written as ax² + bx + c = 0, where a, b, and c are numbers and a cannot be 0.

• a is the coefficient of x².
• b is the coefficient of x.
• c is the constant number.

This tool can help you solve ax squared plus bx plus c and find x intercepts when the roots are real.

Quadratic Formula

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

The plus-minus symbol means the equation may have two answers. One answer uses addition, and the other answer uses subtraction.

What Is the Discriminant?

The discriminant is b² - 4ac. It tells you what type of answer the quadratic equation has.

• If the discriminant is greater than 0, there are two real roots.
• If the discriminant is equal to 0, there is one repeated real root.
• If the discriminant is less than 0, there are two complex roots.

Quadratic Formula Example

Solve: x² - 5x + 6 = 0

Identify:

• a = 1
• b = -5
• c = 6

Discriminant:

D = (-5)² - 4(1)(6)
D = 25 - 24
D = 1

Formula:

x = (5 ± √1) / 2

Answers: x = 3 and x = 2

When Should You Use the Quadratic Formula?

The quadratic formula is useful when factoring is difficult or when you need an exact solution. It works for all quadratic equations as long as a is not zero. Many students use it to solve quadratic equation problems in algebra classes, test prep, and homework assignments.

Real Roots vs Complex Roots

Real roots are answers that can be placed on a normal number line. If a quadratic equation has real roots, those roots are also the x-intercepts of the graph.

Complex roots include the imaginary number i. These happen when the discriminant is negative. In simple terms, the graph does not cross the x-axis when the roots are complex.

Common Mistakes When Solving Quadratic Equations

• Forgetting that a cannot be 0.
• Using the wrong sign for b.
• Forgetting to square b.
• Making mistakes with negative numbers.
• Forgetting the ± symbol.
• Rounding too early.

Who Can Use This Calculator?

This quadratic formula calculator is helpful for middle school students, high school algebra students, college algebra students, parents helping with homework, teachers creating examples, and SAT or ACT test prep students.