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

What does the symbol '≥' indicate in quadratic inequalities?

Back

'≥' indicates 'greater than or equal to', meaning the value can be equal to the boundary or greater.

Front

What does the symbol '>' indicate in quadratic inequalities?

Back

'>' indicates 'greater than', meaning the value must be strictly greater than the boundary.

Front

How do you solve a quadratic inequality?

Back

1. Solve the corresponding quadratic equation. 2. Determine the intervals based on the roots. 3. Test each interval to see where the inequality holds true.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the interval notation (-3, 4) represent?

Back

It represents all real numbers greater than -3 and less than 4, excluding -3 and 4.

Front

What does the interval notation [-3, 4] represent?

Back

It represents all real numbers from -3 to 4, including both -3 and 4.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

How do you graph a quadratic inequality?

Back

1. Graph the corresponding quadratic equation. 2. Determine if the parabola is solid (≤ or ≥) or dashed (< or >). 3. Shade the appropriate region based on the inequality.

Front

What is the solution set of the inequality 2x² + 5x ≥ 12?

Back

The solution set is (−∞, -4] U [1.5, ∞).