solving quadratic inequalities

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SOLVING QUADRATIC INEQUALITIES Adapted from Walch Education

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Solving Quadratic Inequalities. Adapted from Walch Education. Quadratic Inequalities. 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. - PowerPoint PPT Presentation

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Solving Quadratic Inequalities

Solving Quadratic InequalitiesAdapted from Walch Education

Quadratic InequalitiesQuadratic inequalities can be written in the form ax2 + bx + c < 0, ax2 + bx + c 0, ax2 + bx + c > 0, or ax2 + 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.5.2.5: Solving Quadratic Inequalities22Key ConceptsThe 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. 5.2.5: Solving Quadratic Inequalities3Key Concepts, continuedSolutions 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 < or >.Graph endpoints as a closed dot if the original inequality symbol is or .

5.2.5: Solving Quadratic Inequalities4Practice # 1For what values of x is (x 2)(x + 10) > 0?5.2.5: Solving Quadratic Inequalities5Determine the sign possibilitiesThe expression will be positive when both factors are positive or both factors are negative. 5.2.5: Solving Quadratic Inequalities6Determine when both factors are positivex 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 > 2. 5.2.5: Solving Quadratic Inequalities7Determine when both factors are negativex 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 < 10.5.2.5: Solving Quadratic Inequalities8Your TurnSolve x2 + 8x + 7 0. Graph the solutions on a number line.5.2.5: Solving Quadratic Inequalities9Thanks for Watching!Ms. Dambreville