Quadratic & Rational Inequalities Test #5

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In this section we learn how to solve quadratic and rational inequalities. When solving a quadratic inequality, we must lean on our knowledge of quadratic
equations along with linear inequalities. One method we can use to solve a quadratic inequality is graphing. As we have seen before, graphing is not a
practical method for finding solutions. Alternatively, we can turn to a more practical approach which involves using test numbers. For this approach, we
write our quadratic inequality as an equation and solve. Once this is done, we then use the solutions to divide the number line into intervals. We then
test inside each interval to find which intervals satisfy the inequality. If one number inside the interval satisfies the inequality, then the whole
interval does. Lastly, we must consider the endpoints. These are included in the solution set if we have a non-strict inequality and not included if we
have a strict inequality. We use a similar approach to solve a rational inequality. We write our rational inequality so that zero is on one side and there
is a single rational expression on the other. Then we determine the numbers that will make the numerator or denominator equal to zero. After this we use these numbers
to divide the number line into intervals. We find the intervals that satisfy our inequality by testing a number from each interval. Lastly, we consider our
endpoints. These are included in the solution set if we have a non-strict inequality and not included if we have a strict inequality. We must exclude any
values that make the denominator zero.

Quadratic & Rational Inequalities Resources:

Videos:

Khan Academy - Video
Khan Academy - Video
Virtual Nerd - Video
Text Lessons:

WTAMU - Text Lesson
Cliffs Notes - Text Lesson
Purple Math - Text Lesson
Worksheets:

Kuta - Worksheet
Kuta - Worksheet
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