Adapted from Walch Education

 Quadratic inequalities can be written in the form ax 2 + bx + c < 0, ax 2 + bx + c ≤ 0, ax 2 + bx + c > 0, or ax 2 + bx + c ≥ 0.  The solutions to quadratic inequalities are written as intervals.  An interval is the set of all real numbers between two given numbers.  The two numbers on the ends are the endpoints. The endpoints might or might not be included in the interval depending on whether the interval is open, closed, or half- open : Solving Quadratic Inequalities2

 The solutions to a quadratic inequality can be one interval or two intervals.  Use these solutions to create regions on a number line and test points in each region to solve the inequality.  If the quadratic equation has only complex solutions, the expression is either always positive or always negative. In these cases, the inequality will have no solution or infinitely many solutions : Solving Quadratic Inequalities3

Solutions of quadratic inequalities are often graphed on number lines. The endpoints of the solution interval are represented by either an open dot or a closed dot. Graph the endpoints as an open dot if the original inequality symbol is. Graph endpoints as a closed dot if the original inequality symbol is ≤ or ≥ : Solving Quadratic Inequalities4

 For what values of x is ( x – 2)( x + 10) > 0? 5.2.5: Solving Quadratic Inequalities5

 The expression will be positive when both factors are positive or both factors are negative : Solving Quadratic Inequalities6

 x – 2 is positive when x > 2.  x + 10 is positive when x > –10. Both factors are positive when x > 2 and x > –10, or when x > : Solving Quadratic Inequalities7

 x – 2 is negative when x < 2.  x + 10 is negative when x < –10. Both factors are negative when x < 2 and x < –10, or when x < –10. ( x – 2)( x + 10) > 0 when x > 2 or x < – : Solving Quadratic Inequalities8

 Solve x x + 7 ≤ 0. Graph the solutions on a number line : Solving Quadratic Inequalities9

Ms. Dambreville