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1
Quadratic
Inequalities
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Quadratic Inequality
2 ways to solve:
1 graph the inequality and find the region
2 use "sign" diagram to find solution
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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
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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
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x2 + x + 1 > 0 Graph and solve the inequality
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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
5. Determine the intervals for which values are true for the inequality
4. Test one value of x for each interval determined by the zeros
greater than zero so we are looking for the intervals that make x2 + 5x + 6 positive
10 2 3 4 5 6 7 8 9 1012345678910
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Solve by graphing
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10 2 3 4 5 6 7 8 9 1012345678910
Make a sign diagram and state the intervals that satisfy the inequality
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Solve graphically
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10 2 3 4 5 6 7 8 9 1012345678910
Make a sign diagram and state the intervals that satisfy the inequality
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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 xaxisthe function f(x) is then negative
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Exercise 28
Questions 1 - 3