VECTOR LAB
Your first experiment

Choose a formula. Change a value. Inspect what moves.

The result, worked steps, and live model stay connected. Start with any subject—the calculations stay on this device.

Quadratic Equation Calculator

Write the equation as ax² + bx + c = 0 before entering its coefficients. The discriminant b² − 4ac determines whether there are two, one, or no real roots.

Worked example: For x² − 5x + 6 = 0, the discriminant is 25 − 24 = 1. The roots are (5 ± 1)/2: 2 and 3. The main result reports the larger real root, 3.

Assumptions and units: The coefficient a must be nonzero. Negative discriminants have complex roots, which this real-root tool does not calculate. The relationship graph plots the larger root, not the original parabola.

Read the full lesson and self-check

calculated in real time

Select a formula, tune the variables, and see the model respond. No black box — just a clearer way to think.

active module
Math / Quadratic root
Math / instrument

Larger quadratic root

Find the larger real root of ax² + bx + c = 0.

x₊, x₋ = (−b ± √Δ) ÷ 2a; larger = max(x₊, x₋)
Live 3D graph
Larger quadratic root live 3D graphA two-input result surface, not a physical object. Each axis has its own scale. Held fixed: Constant c = 6. Gaps indicate undefined samples or magnitudes ≥ 10¹². This graph plots the larger real root, using the same calculation as the solver. Axes: Coefficient a, Coefficient b, Larger real root. Larger quadratic root: 3 00.511.52Coefficient a-8-6-4-2Coefficient b050Larger real rootCurrent result: 3
Live inputs
24° tilt / -35° orbit / 1.00x
  • Coefficient a: 0 to 2
  • Coefficient b: -8.75 to -1.25
  • Larger real root: -8.681 to 95.49
  • Live value marker
  • Result graph (independent scales)

A two-input result surface, not a physical object. Each axis has its own scale. Held fixed: Constant c = 6. Gaps indicate undefined samples or magnitudes ≥ 10¹². This graph plots the larger real root, using the same calculation as the solver.

Drag to orbit. Focus the graph and use arrow keys to rotate, +/− to zoom, or 0 to reset. Axis ranges adjust to keep the data in view.

Larger quadratic root: 3

model notes

Each point uses the same formula as the calculator. Choose the input axes to explore a result curve or surface; the other inputs stay fixed. The amber marker shows your current calculation.

Graph updates
Live with every input
Object type
Larger quadratic root
Press and drag anywhere on the model to inspect it from a new angle.
Live result
3
step by step
  1. 01Discriminant Δ = (-5)² − 4 × 1 × 6 = 1
  2. 02Both roots: x₊ = 3; x₋ = 2
  3. 03Larger real root = max(x₊, x₋) = 3
unit converter
Converted result
100 cm
Learn from the result

A calculator that explains the numbers

Use Vector Lab as a visual study companion: change one variable, inspect the model, and connect the substitution steps to the result. The best way to learn a formula is to see which inputs actually control it.

Study the formulas: lessons and worked examples

Start with units

Check that quantities belong together before calculating. Use the converter when a problem gives measurements in different units.

Change one input

Vary one number while holding the others steady. This makes proportional, squared, and inverse relationships easier to recognize.

Read the steps

The worked substitution shows how the formula becomes a result. Compare it with your own setup before moving to the next problem.

Are the results saved?

Recent runs and practice progress are saved locally in this browser. No account is required, and the current calculator does not send those values to a server.

Can I use it for homework?

Yes, as a study companion. Use the steps and model to understand the setup, then verify the answer with your class materials or instructor.