Quadratic Equation Calculator

Use this quadratic equation calculator to solve ax² + bx + c = 0. Enter a, b and c to see solutions and a clear graph. You will see the discriminant and the vertex too.

How It Works

Type numbers in the fields. The calculator uses the quadratic formula when a has a nonzero value. If a equals zero and b has a value, it solves a linear equation. If a, b and c are zero, every x satisfies the equation. If a and b are zero and c has a value, no solution exists.

The formatted equation appears near the top. The graph shows the curve on a grid with x and y axes. A red dot marks each solution on the x axis when it exists. The scale label tells you the visible range. Results update as you type or when you click Calculate.

Δ is the discriminant. It equals b squared minus 4ac. The discriminant shows the number and type of solutions. The vertex is the highest or lowest point of the curve.

Step-by-Step Guide

1. Review the default values a equals 1 and b equals -3 and c equals 2.
2. Enter a, which multiplies x².
3. Enter b, which multiplies x.
4. Enter c, the constant term.
5. Click Calculate to update results and the graph.

• a controls the curve opening and width. Use a nonzero value for a quadratic.
• b shifts the curve sideways. Any number works.
• c shifts the curve up or down. Any number works.
• Use integers or decimals. Negative numbers work for any field.

Why You'll Love It

This quadratic equation calculator gives clear results fast. You see the formatted equation, the discriminant, solutions, and the vertex in one view. The graph adds context and marks solution points with bright dots.

• Equation preview updates as you edit entries.
• Discriminant value shown for every solve.
• Complex solutions written with i for clarity.
• Vertex printed with opening direction up or down.
• Graph shows the curve and highlights solution points.

Instant Math Made Easy

Get more value with a few quick tips.

• Test a simple case by setting a to 1.
• Try nearby values to check your work.
• Use decimals to model fractions.
• Flip the sign of a to see the curve turn.
• Watch the scale note to judge the viewing window.

Inside the Calculator

The calculator follows standard rules from algebra. The discriminant Δ equals b squared minus 4ac. Two distinct solutions appear when Δ is greater than zero. One repeated solution appears when Δ equals zero. Two complex solutions appear when Δ is less than zero.

When a equals zero and b has a value, the equation is linear. The single solution is x equals negative c divided by b. When a, b and c are zero, every x works. When a and b are zero and c has a value, there is no solution.

The vertex x value equals negative b divided by two times a. The vertex y value equals ax² + bx + c at that x. If a is positive, the curve opens up. If a is negative, the curve opens down.

Numbers round to four decimal places when needed. Whole numbers display without decimals. The graph draws axes and a grid. It labels a symmetric range for x and y.

Code at a Glance

Output guide for quick reading.

• Equation line shows your inputs in standard form.
• Discriminant line prints Δ and its value.
• Solutions line prints x values, or complex pairs with i.
• Vertex line prints the coordinates.
• Opens line states up or down based on a.
• Graph info line shows the scale range.

In a Nutshell

This quadratic equation calculator gives correct answers, a clear graph, and helpful context. It works well for study, teaching, and quick checks.

• Inputs accept integers and decimals. Use 0.3333 in place of one third.
• Values round to four decimals when needed.
• Solution dots appear only when Δ is at least zero.
• When a and b are zero, the graph area states Not a function in x.
• Very large numbers can reduce detail. The canvas shows a wide range in that case.

Common use cases include these tasks.

• Finish algebra homework with fast checks.
• Factor by finding solutions, then write factors as x minus r.
• Model projectile height with y equals ax² + bx + c.
• Find the vertex for max or min problems.
• Explore how changing a, b and c shifts the curve.

Quick examples help lock it in. With a equals 1 and b equals -3 and c equals 2, the solutions are 1 and 2. With a equals 1 and b equals 2 and c equals 5, you get complex solutions at -1 plus 2i and -1 minus 2i. With a equals 0 and b equals 2 and c equals 4, the linear solution is x equals -2.