Quadratic Inequalities

Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax² + bx + c < 0, ax² + bx + c > 0, ax² + bx + c ≤ 0, or ax² + bx + c ≥ 0.

Front

How do you solve a quadratic inequality?

Back

To solve a quadratic inequality, first solve the corresponding quadratic equation to find the critical points. Then, test intervals between these points to determine where the inequality holds true.

Front

What does the graph of a quadratic inequality represent?

Back

The graph of a quadratic inequality represents the set of all points (x, y) that satisfy the inequality, typically shown as a shaded region above or below the parabola.

Front

What is the significance of the critical points in quadratic inequalities?

Back

Critical points are the x-values where the quadratic expression equals zero. They divide the number line into intervals that can be tested to determine where the inequality is satisfied.

Front

Solve: 2x² + 5x ≥ 12

Back

x ≤ -4 or x ≥ 1.5

Front

Is (2, 3) part of the solution set for y < 2x² - 3x + 1?

Back

No

Front

Which inequality is represented by the graph? y > (x + 3)² - 3

Back

y > (x + 3)² - 3

Front

Which inequality is represented by the graph? y > -(x - 4)² + 1

Back

y > -(x - 4)² + 1

Front

Solve: 3x - x² > 0

Back

0 < x < 3

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) include the boundary points.