5.7 Quadratic Inequalities

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5.7 Quadratic Inequalities

  1. 1. 5.7 Graphing and SolvingQuadratic Inequalities
  2. 2. 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.
  3. 3. Example: Graph y > x2 – 2x – 3 Remember, find the vertex!
  4. 4. Your Turn! Graph y 2x2 - 5x – 3
  5. 5. Graphing a System Graph both inequalities on the same grid. Solutions are where the shading overlaps. Example: Graph
  6. 6. 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)
  7. 7. Solving by Graphing Solve x2 – 6x + 5 < 0Solution:1<x<5
  8. 8. Example: Solve 2x2 + 3x – 3 0
  9. 9. Your Turn! Solve -x2 – 9x + 36 > 0
  10. 10. 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”
  11. 11. Example: Solve x2 + 2x 8
  12. 12. Your Turn! Solve 2x2 – x > 3

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