Graphing Quadratic Inequalities Calculator

This tool visualizes the solution set for a quadratic inequality in the form \(y \ R \ ax^2 + bx + c\), where R is an inequality symbol.

Steps to Graph:

• 1. Graph the Parabola: First, the boundary line is drawn using the equation \(y = ax^2 + bx + c\).
• 2. Choose Line Style:
  • A solid line is used for \(\geq\) (greater than or equal to) and \(\leq\) (less than or equal to). This indicates that points on the parabola are included in the solution.
  • A dashed line is used for \(>\) (greater than) and \(<\) (less than). This means points on the parabola are not part of the solution.
• 3. Shade the Region: A region of the graph is shaded to show all pairs of (x, y) that satisfy the inequality.
  • For \(y > ...\) or \(y \geq ...\), the area above the parabola is shaded.
  • For \(y < ...\) or \(y \leq ...\), the area below the parabola is shaded.

The calculator automatically identifies key features like the vertex (the highest or lowest point), the roots (where the parabola crosses the x-axis), and the y-intercept.