What is the solution set for the inequality $$x(5 - 10x)

The solution set is $$y \frac{1}{2}$$ .

What is the solution set for the inequality $$(x-4)(4x-5) \ge 0$$ ?

The solution set is $$x \le \frac{5}{4}$$ or $$x \ge 4$$ .

What is the solution set for the inequality $$(5x+6)(7x-9)

The solution set is $$-\frac{6}{5}

What is the solution set for the inequality $$x(6x+3) \le 0$$ ?

The solution set is $$-\frac{1}{2} \le x \le 0$$ .

Explain how to graph a quadratic inequality.

To graph a quadratic inequality, first graph the corresponding quadratic equation as a parabola, then determine the regions that satisfy the inequality by testing points or using the sign of the quadratic expression.

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

Strict inequalities (e.g., ) do not include the boundary points, while non-strict inequalities (e.g., ≤, ≥) include the boundary points in the solution set.

How can you check if a value is part of the solution set of a quadratic inequality?

To check if a value is part of the solution set, substitute the value into the quadratic expression and see if the resulting inequality holds true.

What role do test points play in solving quadratic inequalities?

Test points are used to determine the sign of the quadratic expression in each interval created by the roots, helping to identify which intervals satisfy the inequality.

Quadratic inequality Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Define a quadratic inequality.

Back

2.

FLASHCARD QUESTION

Front

What is the general form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

How do you find the roots of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

5.

FLASHCARD QUESTION

Front

What is the significance of the vertex in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

How do you determine the intervals of a quadratic inequality?

Back

To determine the intervals of a quadratic inequality, first find the roots of the corresponding quadratic equation, then test the sign of the quadratic expression in the intervals defined by these roots.

7.

FLASHCARD QUESTION

Front

Back

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