Quadratic functions

1003148601

Level:

Consider an object thrown upwards from the ground with the initial velocity of

30 \frac{m}{s}

. The object moves upwards with decreasing vertical velocity until it stops. Then it starts moving vertically downwards. Find the greatest height above the ground the object does reach.

Note: The vertical distance

y

of a thrown object is described by the equation

y = v_{0} t - \frac{1}{2} g t^{2}

, where

v_{0}

is the initial velocity of the thrown object,

g

is gravitational acceleration (count with the rounded value

10 \frac{m}{s^{2}}

), and

t

is the time period of the object motion in seconds.

45 m

135 m

360 m

40 m

1003158902

Level:

The length of a rectangle is

4 cm

and width is

x cm

. The rectangle is divided by vertical crossing line into two parts so that one part is a square with the side of

x cm

(see the picture). What is the maximum area of the remaining part of the rectangle?

4 {cm}^{2}

2 {cm}^{2}

16 {cm}^{2}

1 {cm}^{2}

1003158901

Level:

An object is moving with a constant deceleration in a straight line. Displacement

s

(in metres) in time

t

(in seconds) is modelled by

s = 24 t - 3 t^{2}

. Find the displacement of the object from the moment it starts to decelerate until it stops.

48 m

144 m

16 m

96 m

1103120010

Level:

Let

f (x) = (x + a)^{2} + b

and

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

, where

a

b \in R

. In which of the next four given pictures are the graphs of both functions

f

and

g

1103120009

Level:

In the picture there are two parabolas. One parabola can be mapped onto the other by shifting. These parabolas are graphs of the quadratic functions

f (x) = - (x - a)^{2} + b and g (x) = - (x - c)^{2} + d,

where

a

b

c

d \in R

. Following statements describe the relations between the pairs of the coefficients

a

b

c

and

d

. Choose the true statement.

a = c - 1 \land b = d + 4

a = c + 1 \land b = d - 4

a = c - 4 \land b = d + 1

a = c + 4 \land b = d - 1

1103120008

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)^{2} + 4

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

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

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

1103120007

Level:

Let

f (x) = x^{2}

. Given the graph of the function

f

and the graph of a function

g

which was obtained by shifting the graph of

f

(see the picture), choose the function

g

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

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

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

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

1103120006

Level:

In the picture A, we are given the graph of the quadratic function

f (x) = x^{2}

. Use the graph of

f

as help to identify which of the graphs given in the picture B is the graph of

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

. Choose what is the colour of the graph of

g

blue

red

yellow

green

1103120005

Level:

In the picture A, we are given the graph of the quadratic function

f (x) = x^{2}

. Use the graph of

f

as help to identify which of the graphs given in the picture B is the graph of

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

. Choose what is the colour of the graph of

g

. (Note: The graphs in the picture B were obtained by shifting and stretching the graph of

f

green

red

blue

yellow

1103120004

Level:

Let

f (x) = x^{2}

. Given the graph of the function

f

and the graph of a function

g

which was obtained as a vertical shift of the graph of

f

(see the picture), choose the function

g

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

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

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

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

1003148601

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