Graphing Quadratic Inequalities Calculator

Your details

The coefficient of x squared. Set to 0 only if you have a linear expression.
The coefficient of x (the linear term).
The constant term in the quadratic expression.
The comparison direction. Use <= or >= to include boundary points in the solution.
The value on the right side of the inequality. Usually 0, but any real number works.
Solution setOne interval
(1, 2)

The solution in interval notation

Discriminant1
Vertex x-coordinate1.5
Vertex y-value-0.25
Root 1 (x₁)1
Root 2 (x₂)2
Number of real roots2

Solution: (1, 2)

  • The discriminant is 1.0000, which is positive, so the parabola crosses the x-axis at two real points.
  • The parabola opens upward (a > 0), so the quadratic is negative only between its two roots (if they exist).
  • Because the inequality is strict (< or >), the boundary points (the roots) are excluded from the solution.

Next stepSubstitute a value inside the interval you found back into the original inequality to verify the solution is correct.

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