Quadratic functions

1103034604

Level:

Given graphs of the functions

f (x) = - 2 x^{2} + 5 x + 3

and

g (x) = 2 x + 1

, find the solution set of the following inequality.

- 2 x^{2} + 5 x + 3 < 2 x + 1

(- \infty; - 0.5) \cup (2; \infty)

(- 0.5; 2)

(- \infty; - 0.5) \cup (3; \infty)

(- 0.5; 3)

1103034603

Level:

Given graphs of the functions

f (x) = x^{2} - 6 x + 8

and

g (x) = - 2 x + 4

, find the solution set of the following inequality.

x^{2} - 6 x + 8 \geq - 2 x + 4

R

(- \infty; 2] \cup [4; \infty)

{2}

[2; 4]

1103034602

Level:

Given graphs of the functions

f (x) = x^{2} - 6 x + 8

and

g (x) = 2 x + 1

, find the solution set of the following inequality.

x^{2} - 6 x + 8 > 2 x + 1

(- \infty; 1) \cup (7; \infty)

(1; 7)

(- \infty; 2) \cup (4; \infty)

(1; \infty)

1103034601

Level:

Given graphs of the functions

f (x) = x^{2} - 6 x + 8

and

g (x) = - x^{2} - 2 x + 24

, find the solution set of the following inequality.

x^{2} - 6 x + 8 \leq - x^{2} - 2 x + 24

[- 2; 4]

[2; 4]

[0; 24]

[- 6; 4]

9000033707

Level:

Identify the inequality with a solution graphed in the picture.

| x (3 - x) | > 3 - x

| x (x - 3) | < x - 3

| 3 x - x^{2} | > x - 3

| x^{2} - 3 x | < 3 - x

x^{2} - 3 | x | > 3 - x

x^{2} - 3 | x | < x - 3

9000025610

Level:

Identify a quadratic equation which is solved by a graphical method in the picture.

x^{2} - 6 x + 9 = 0

x^{2} + 9 x - 3 = 0

x^{2} - 9 x - 3 = 0

x^{2} + 6 x + 9 = 0

9000022302

Level:

Complete the following statement, if possible: „The function

f : y = - x^{2} - 2 x + 15

attains only ... values on the interval

[- 5; 3]

.”

nonnegative

positive

negative

neither of the above is valid

9000022307

Level:

Using the graph of the function

f (x) = x^{2} - x - 6

solve the system of inequalities.

- 4 < x^{2} - x - 6 < 0

(- 2; - 1) \cup (2; 3)

(- 2; 3)

(- \infty; - 2) \cup (3; \infty)

(- \infty; - 1) \cup (2; \infty)

9000022308

Level:

Using graphs of the functions

f (x) = - 2 x^{2} + 3 x + 4

and

g (x) = x

solve the following quadratic inequality.

- 2 x^{2} + 3 x + 4 \geq x

[- 1; 2]

{- 1; 2}

(- 1; 2)

(- \infty; - 1) \cup (2; \infty)

9000022309

Level:

Using graphs of the functions

f (x) = x^{2} + x - 1

and

g (x) = - \frac{1}{2} x

solve the following quadratic inequality.

x^{2} + x - 1 > - \frac{1}{2} x

(- \infty; - 2) \cup (\frac{1}{2}; \infty)

(- 2; \frac{1}{2})

[- 2; \frac{1}{2}]

(- \infty; - 2] \cup [\frac{1}{2}; \infty)

1103034604

1103034603

1103034602

1103034601

9000033707

9000025610

9000022302

9000022307

9000022308

9000022309

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