This document discusses two methods for solving quadratic inequalities: graphing and using a sign diagram. For graphing, the inequality is graphed like a boundary line and the range where the inequality is true is shaded. For the sign diagram method, the zeros of the quadratic function are placed on a number line and the intervals where the function has the same sign as the inequality are determined to be the solution set. Examples of both methods are shown and key aspects like critical numbers and sign changes are explained.

1. Quadratic
Inequalities
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2. 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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3. 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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4. 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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5. x2 + x + 1 > 0 Graph and solve the inequality
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6. 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
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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
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7. Solve by graphing
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8. Make a sign diagram and state the
intervals that satisfy the inequality
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9. Solve graphically
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10. 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
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11. 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
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12. Exercise 28
Questions 1-3
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