Quadratic Inequalities Flashcards

An inequality involving a quadratic expression, such as ax² + bx + c > 0.

ax² + bx + c > 0, ax² + bx + c < 0, ax² + bx + c ≥ 0, or ax² + bx + c ≤ 0.

1. Rearrange into standard form. 2. Solve the corresponding quadratic equation. 3. Use a sketch or test values to determine the solution.

The solutions to the corresponding quadratic equation ax² + bx + c = 0, used to divide the number line into intervals.

Substitute a value from each interval into the quadratic expression to determine where the inequality holds true.

The solution is where the graph of y = ax² + bx + c is above the x-axis.

The solution is where the graph of y = ax² + bx + c is below the x-axis.

Include the critical values in the solution, as the inequality allows for equality.

A parabola that opens upwards if a > 0 and downwards if a < 0.

Expressed as a range of x-values, e.g., x < -2 or x > 3, or -1 ≤ x ≤ 4.