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Solved problems for the chapter:

Quadratic inequalities

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Quadratic inequality

1. Leading coefficient a > 0 (function facing up)

1.1. D > 0 (the function has two real zeros)

1.2. D = 0 (the function has a repeated real zero)

1.3. D < 0 (function has no real zeros)

2. Leading coefficient a < 0 (downward facing function)

2.1. D > 0 (the function has two real zeros)

2.2. D = 0 (function has a repeated real zero)

2.3. D < 0 (function has no real zeros)

3. Forum

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Function and its property for KS4

1. Dependent and independent variable

1.1. Domain of a function

1.2. Range

2. Presentation of the function

2.1. Function rules

2.2. Function tabulation

2.3. Arrow diagram

2.4. Function graph

3. The x-intercept and the y-intercept

3.1. X-intercept

3.2. Zeros of a polynomial

3.2.1. Even zeros

3.2.2. Odd Zeros

3.3. y-intercepts

4. Injectivity, surjectivity and bijectivity

4.1. Injective function

4.2. Surjective function

4.3. Bijective function

5. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:quadratic_inequalities/5389/

Example 1.

For what values of will the function:

be negative?

Example 2.

Solve the inequality .

Compare the numbers a and b and insert the symbols >, < or = in the middle column (see the first two solved examples).

For what values of will the function:

have positive values?

Solve the rational inequality:

For what values of will the function:

be non-negative values?

For what values does the function

have non-negative values?

For what values of will the function

have negative values?

Draw a graph of a rational function:

Where is the function negative?

10.

Solve the inequality .

11.

For what values of will the function:

take positive values?

12.

Solve the rational inequality:

13.

Solve the inequality .

14.

The function is given.

Draw the graph of f(x).
Solve the inequality .

15.

A rational function is given below:

Draw a graph of the function and use the graph to determine for what values of will the function be less than .

16.

Solve the inequality .

17.

Solve the inequality .

18.

Solve the rational inequality:

19.

Solve the rational inequality:

20.

Solve the rational inequality:

21.

Solve the system of inequalities , .

22.

Solve the rational inequality:

23.

Solve the inequality .

24.

Solve the rational inequality:

25.

Solve the inequality .

26.

Solve the rational inequality:

27.

Solve the inequality .

28.

Solve the inequality .

29.

Solve the inequality .

30.

Solve the inequality .

31.

Solve the inequality .

32.

Solve the inequality .

33.

Solve the system of inequalities:

34.

Solve the system of inequalities , .

35.

Draw the set of points (x, y) that satisfy the conditions .

36.

Solve the inequality .

37.

For which values x applies:

38.

Solve the inequality . Write the set of solutions as an interval and illustrate it on a number line.