Nov. 16 Quadratic Inequalities
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Nov. 16 Quadratic Inequalities

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    Nov. 16 Quadratic Inequalities Nov. 16 Quadratic Inequalities Document Transcript

    • Quadratic  Inequalities 1
    • Quadratic Inequality 2 ways to solve:  1 ­ graph the inequality and find the region 2 ­ use "sign" diagram to find solution 2
    • Solve by graphing: 1. Graph the inequality using the same rules for the     boundary line as used with linear inequalities 2. Test one point on each side of the boundary line to     determine the range that is true for the inequality. 3. Shade in the range 3
    • 1. Graph by finding the zeros and the vertex 2. Test one value inside the parabola and one outside 3. Shade in the area that has the value of x that makes  the inequality true 4
    • x2 + x + 1 > 0 Graph and solve the inequality 5
    • Sign Diagram 1. Determine the zeros of the function and place them on     a number line. 2. Use open circles for > or < 3. Use solid circles for      or     ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10 4. Test one value of x for each interval determined by      the zeros 5. Determine the intervals for which values are true     for the inequality greater than zero so we are  looking for the intervals that make  x2 + 5x + 6 positive 6
    • Solve by graphing 7
    • Make a sign diagram and state the  intervals that satisfy the inequality ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10 8
    • Solve graphically 9
    • Make a sign diagram and state the  intervals that satisfy the inequality ­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1 0 1 2 3 4 5 6 7 8 9 10 10
    • The zeros of the function are known as the critical numbers They determine the test intervals for the function These are also the points were the function changes sign If the function is above the x­axis the value of the function f(x) is  positive If the function crosses the x­axis and is then below the x­axis the function f(x) is then negative 11
    • Exercise  28 Questions 1-3 12