Quadratic inequalities

Use zeros and signs of quadratics to find solution intervals.

Meaning

Quadratic inequalities ask where a quadratic is positive or negative. Consider its zeros and opening direction, or the signs of its factors.

Example

For the factors must have opposite signs, giving Substituting checks The interval between roots is not always the answer. It depends on the inequality direction, leading coefficient, and whether equality is included.

Practice for this concept

Scope and references

Topics

Quadratic graphs and signs, boundary values, solution intervals

Learning goal

Use zeros and signs of quadratics to find solution intervals.

Helpful background

Connect quadratic roots with the graph's sign.