Quadratic Calculator
Solve quadratic equations using multiple methods - quadratic formula, factoring, completing the square, and graphing with detailed step-by-step solutions.
Solutions
Step-by-Step Solution
Discriminant Analysis
Common Quadratic Examples
x² - 5x + 6 = 0
Two real solutions
x² - 4x + 4 = 0
One solution (repeated)
x² - 4 = 0
Perfect square
x² + 4 = 0
No real solutions
Solution Methods Comparison
| Method | Best Used When | Advantages | Example |
|---|---|---|---|
| Quadratic Formula | Always works for any quadratic | Universal method, shows discriminant | 2x² + 3x - 1 = 0 |
| Factoring | Integer coefficients, factorable | Quick and elegant when possible | x² - 5x + 6 = 0 |
| Completing the Square | Finding vertex form | Shows vertex, useful for graphing | x² + 6x + 5 = 0 |
| Graphing | Visual understanding needed | Shows parabola shape and properties | Any quadratic function |
Practical Applications
Physics & Motion
Calculate projectile motion, free fall problems, and optimize trajectories using quadratic equations.
Business & Economics
Optimize profit functions, calculate break-even points, and analyze cost-revenue relationships.
Engineering
Design parabolic structures, optimize dimensions, and solve structural engineering problems.
Agriculture
Optimize crop yields, calculate fertilizer applications, and design irrigation systems.
Architecture
Design arches, bridges, and optimize building dimensions for maximum area or minimum cost.
Education
Learn algebra concepts, understand parabolas, and solve mathematical word problems.
Quadratic Calculator Answers
What does the quadratic calculator do?
It solves quadratic equations by calculating the roots using the quadratic formula, factoring, or completing the square.
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree two in the form ax² + bx + c = 0, where a ≠ 0.
Can it find complex roots?
Yes. The calculator provides real or complex roots depending on the discriminant value.
Does it offer step-by-step solutions?
Many quadratic calculators include detailed steps to help users understand how the solution is derived.