Test: Quadratic inequalities

This test develops methods for solving quadratic inequalities using roots and the sign of a parabola. Tasks cover selecting intervals, handling strict and non-strict boundaries and writing the solution in interval notation.

Question qty: 10
Duration in minutes: 18
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Sample questions

Solve (x − (a))(x − (b)) < 0.
Solve x² < c.
How many integers satisfy a < x < b?
When is a boundary root included in the solution of a strict or non-strict inequality?
Solve x² > c.
Solve (x − (a))(x − (b)) > 0.
Solve (x − (a))(x − (b)) ≤ 0.
Where is y = (x − x₁)(x − x₂), opening upward, negative?

Quadratic inequalities

Solve a quadratic inequality by analysing the sign of ax² + bx + c. First find its zeros, mark them on a number line and determine the sign on every resulting interval.

Parabola method

For a > 0, the parabola is above the x-axis outside two roots and below it between them; for a < 0, the signs reverse. The symbols ≤ and ≥ include roots, while < and > exclude them. With no real roots, the expression has the sign of a everywhere.

Test: Quadratic inequalities

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Sample questions

Quadratic inequalities

Parabola method

Test: Quadratic inequalities

Question Nr. 1 out of 10

Question Nr. 2 out of 10

Question Nr. 3 out of 10

Question Nr. 4 out of 10

Question Nr. 5 out of 10

Question Nr. 6 out of 10

Question Nr. 7 out of 10

Question Nr. 8 out of 10

Question Nr. 9 out of 10

Question Nr. 10 out of 10

Sample questions

Quadratic inequalities

Parabola method

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