Quadratic functions

2000004307

Level:

The function

f

is graphed in the picture. Which of the following is its equation?

f (x) = | x^{2} - 4 |

f (x) = | x^{2} + 4 |

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

f (x) = | x^{2} | + 4

2000004306

Level:

Let

f (x) = x^{2}

. Given the graph of the function

f

and the graph of a function

g

(see the picture), choose the function

g

g (x) = - x^{2} + 4

g (x) = x^{2} - 4

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

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

2000004305

Level:

In the picture A, the graph of the quadratic function

f (x) = x^{2}

is shown. With the aid of the graph of

f

identify which of the graphs shown in the picture B is the graph of

g (x) = x^{2} - 2 x - 3 = (x + 1) (x - 3)

. What is the color of the graph of

g

? (Note: Each graph in the picture B was obtained by shifting the graph of

f

blue

red

yellow

green

2000004304

Level:

In the picture A, the graph of the quadratic function

f (x) = x^{2}

is shown. With the aid of the graph of

f

identify which of the graphs shown in the picture B is the graph of

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

. What is the color of the graph of

g

? (Note: Each graph in the picture B is the graph of some transformation of

f

yellow

red

green

blue

2000004303

Level:

In the picture A, the graph of the quadratic function

f (x) = x^{2}

is shown. With the aid of the graph of

f

identify which of the graphs shown in the picture B is the graph of

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

. What is the color of the graph of

g

? (Note: Each graph in the picture B was obtained by shifting the graph of

f

red

green

yellow

blue

2000004302

Level:

In the picture A, the graph of the quadratic function

f (x) = x^{2}

is shown. With the aid of the graph of

f

identify which of the graphs shown in the picture B is the graph of

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

. What is the color of the graph of

g

? (Note: Each graph in the picture B is the graph of some transformation of

f

green

blue

yellow

red

2000004301

Level:

Find the intervals of monotonicity of the quadratic function

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

The function is increasing on

(- \infty; 0]

and decreasing on

[0; + \infty)

The function is increasing on

(- \infty; 4]

and decreasing on

[4; + \infty)

The function is decreasing on

(- \infty; 0]

and increasing on

[0; + \infty)

The function is decreasing on

(- \infty; 4]

and increasing on

[4; + \infty)