Quadratic Inequalities in TwoVariables Four types: To graph:1. Draw the parabola. >,< : dashed line , : solid line2. Choose a point from the inside and plug it in3. If true, shade inside. If false, shade outside.
Example: Graph y > x2 – 2x – 3 Remember, find the vertex!
Graphing a System Graph both inequalities on the same grid. Solutions are where the shading overlaps. Example: Graph
Quadratic Inequalities in One Variable Can be solved using a graph. To solve ax2 + bx + c < 0 (or 0), graph the parabola and identify on which x-values the graph lies below the x-axis. To solve ax2 + bx + c > 0 (or 0), identify on which x-values the graph lies above the x-axis. Find the intercepts by solving for x.(Remember: solutions = zeros = x-intercepts)
Solving Algebraically1. Write as an equation and solve.2. Plot the solutions (called critical x-values) on a number line.3. Test an x-value in between the critical values. If it is true, solution is an “and” If it is not true, solution is an “or”