What does it mean if a quadratic inequality is satisfied for $$x -1$$ ?

It means that the values of $$x$$ that make the quadratic expression true are either less than -10 or greater than -1.

Solve the quadratic inequality: $$x^2 + 11x + 10 \\geq 0$$ .

The solution is $$x \\leq -10 \\ or \\ x \\geq -1$$ .

Solve the compound inequality: $$3n + 6 > 12 \\ or \\ 4n - 4

The solution is $$n > 2 \\ or \\ n

What is a compound inequality?

A compound inequality is formed by combining two or more inequalities, often using 'and' or 'or' to connect them.

What does the solution $$2 \\leq x \\leq 4$$ represent on a number line?

It represents all values of $$x$$ that are between 2 and 4, inclusive.

What is the significance of critical points in solving inequalities?

Critical points are the values where the expression equals zero or is undefined. They help to divide the number line into intervals for testing.

How do you graph a quadratic inequality?

To graph a quadratic inequality, first graph the corresponding quadratic equation as a boundary. Then, shade the region that satisfies the inequality.

What is the difference between strict and non-strict inequalities?

Strict inequalities ( ) do not include the boundary points, while non-strict inequalities (≤, ≥) do include the boundary points.

What does it mean if a quadratic inequality has no solution?

It means that there are no values of $$x$$ that satisfy the inequality, often occurring when the quadratic expression is always positive or always negative.

Quadratic Inequality and Compound Inequality Flashcards

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1.

FLASHCARD QUESTION

Front

Define a quadratic inequality.

Back

2.

FLASHCARD QUESTION

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What is the general form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

How do you solve a quadratic inequality?

Back

To solve a quadratic inequality, first solve the corresponding quadratic equation to find the critical points. Then, test intervals between these points to determine where the inequality holds true.

4.

FLASHCARD QUESTION

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Back

5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

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7.

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