Last updated: July 31, 2026
Graphing Quadratic Inequalities Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
Discriminant D=b²−4ac; roots x=(-b±√D)/(2a). Combine parabola direction with operator to get solution intervals.
Where:
- a=Coefficient a
- b=Coefficient b
- c=Coefficient c
- operator=Inequality Operator
Worked Examples
Upward parabola, less-than
Solve x²−3x+2 < 0.
- 1Compute D=1
- 2Roots are 1 and 2
- 3For a>0, expression is negative between roots
Upward parabola, greater-or-equal
Solve x²−3x+2 ≥ 0.
- 1Roots remain 1 and 2
- 2For a>0, expression is nonnegative outside roots
- 3Include roots for ≥
No real roots
Analyze x²+2x+5 > 0.
- 1D<0 so no x-intercepts
- 2Parabola opens upward
- 3Expression stays positive for all real x
Introduction
Quadratic inequalities require both roots and sign analysis of the parabola. Enter coefficients and an operator to get interval notation directly.
Formula Overview
Graphing Quadratic Inequalities Calculator uses a deterministic math model based on the calculator logic in calculation.ts.
Discriminant D=b²−4ac; roots x=(-b±√D)/(2a). Combine parabola direction with operator to get solution intervals.
Inputs are validated before computation
Outputs are rounded consistently for readable results
Invalid values return safe fallback outputs
Input Guide
Use each input key exactly as defined below to match calculator wiring and test coverage.
- 1
a: Coefficient a
- 2
b: Coefficient b
- 3
c: Coefficient c
- 4
operator: Inequality Operator
Output Guide
These output IDs map directly to the return object keys in calculation.ts.
- 1
root1: First real root when discriminant is non-negative
- 2
root2: Second real root when discriminant is non-negative
- 3
discriminant: b²−4ac, controls root type
- 4
solutionType: Describes interval behavior of the inequality
- 5
intervalNotation: x-values satisfying the quadratic inequality
Validation Rules
The calculator checks for finite numeric values and applies domain constraints before solving.
Required fields must be present
Domain limits are enforced (for example positive lengths or valid operators)
Invalid or non-finite entries resolve to safe defaults
Use examples to verify expected behavior quickly
How to Use
Enter inputs, run calculation, and interpret the primary output first before reviewing supporting values.
Provide all required inputs
Click calculate
Read primary output first
Use secondary outputs for deeper analysis
Practical Uses
This calculator supports classroom work, engineering checks, and fast verification tasks.
Homework and exam preparation
Design and geometry validation
Spreadsheet cross-checking
Quick scenario analysis
FAQs
What does the Graphing Quadratic Inequalities Calculator compute?
It computes Root 1, Root 2, Discriminant from validated input values.
Which inputs are required?
Required inputs are: Coefficient a, Coefficient b, Coefficient c, Inequality Operator.
How are invalid values handled?
If inputs are invalid or out of domain, the calculator returns safe default outputs instead of invalid math.
Are results rounded?
Yes. Numeric values are rounded in calculation.ts (typically to six decimal places).
Can I use negative or decimal values?
Decimals are accepted where mathematically valid; sign/domain constraints are enforced by the calculator logic.
How can I verify results?
Use the worked examples and compare each output key with manual calculations or trusted references.