Where the parabola crosses above and below the x-axis is the solution to the inequality
If a quadratic equation gives you two roots, a quadratic inequality asks you to use those two roots as boundaries and find the interval where the parabola sits above or below the x-axis. Check it visually first, then try solving it yourself with the quiz.
The solution to the quadratic inequality (x−r₁)(x−r₂) > 0 is the set of x values where the parabola y=(x−r₁)(x−r₂) sits above the x-axis. For < 0, look instead for the x values where it sits below the x-axis.
If the graph opens upward (∪ shape), the region outside the two roots is above the x-axis, and the region between them is below. If it opens downward (∩ shape), it's exactly the opposite.
Use the sliders to change the two roots and the direction the parabola opens, and press the inequality buttons to see how the solution interval shown in green changes.
Root r₁−2
Root r₂3
Find the two roots by factoring, work out whether the graph opens upward or downward, and pick the interval that solves the inequality.
Question 1/10 · 0 correct
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The product of the two roots is the constant term, and the sum of the two roots, with its sign flipped, is the coefficient of x. Use this relationship in reverse to find the two roots quickly.