Graphing Quadratic Inequalities Calculator
MathSolve a quadratic inequality ax^2 + bx + c {>,>=,<,<=} d and find the solution as an interval.
Solution
The solution set of the quadratic inequality, written in interval notation.
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Frequently Asked Questions
How is a quadratic inequality solved?
First find where the parabola ax^2+bx+c equals d (its intersection points with the line y=d) using the quadratic formula. Those points split the number line into regions; the parabola's shape (opening up or down) then determines which regions satisfy the inequality.
What if the inequality has no real solution or is true everywhere?
If the parabola never crosses the line y=d (a negative discriminant), the parabola stays entirely on one side of d. Depending on which side and which inequality was asked, the solution is then either all real numbers or no solution at all.
Why do upward and downward parabolas behave differently?
An upward-opening parabola (a positive) is below the line y=d between its two intersection points and above it outside them. A downward-opening parabola (a negative) is the reverse: above y=d between the points, below it outside them.
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