代数学
Quadratic Inequality Solver: Visualize & Solve ax² + bx + c Inequalities
Solve quadratic inequalities (ax² + bx + c > 0, < 0, ≥ 0, ≤ 0) online with visualization. Understand solutions step-by-step. Free and easy to use!
Enter Coefficients & Inequality
Define the quadratic inequality by entering coefficients and selecting the type.
Inequality:
Solution Interval:
Visualization
Understanding Quadratic Inequalities
A quadratic inequality is an inequality that involves a quadratic polynomial. It takes the form of ax² + bx + c compared to zero using inequality signs such as >, <, ≥, or ≤. Solving a quadratic inequality means finding the set of x values that satisfy the inequality.
This tool helps you solve these inequalities by:
- Visualizing the Parabola: The graph shows the parabola of the quadratic function, helping you see where the function is above or below the x-axis.
- Identifying Solution Intervals: The solution is presented as intervals on the number line, indicating the range of x values that satisfy the inequality.
- Step-by-step Calculation: Although not explicitly shown step-by-step here, the tool performs calculations to find roots and determine the intervals.
Key Terms
- Coefficients (a, b, c): These are the numbers in the quadratic equation. \'a\' determines the parabola's shape, \'b\' affects its position, and \'c\' is the y-intercept.
- Inequality Type: Choose from > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to) to define the inequality.
- Solution Interval: The final output, showing the range(s) of x that satisfy the given quadratic inequality.