Quadratic functions

1003158902

Level: 
C
The length of a rectangle is \( 4\,\mathrm{cm} \) and width is \( x\,\mathrm{cm} \). The rectangle is divided by vertical crossing line into two parts so that one part is a square with the side of \( x\,\mathrm{cm} \) (see the picture). What is the maximum area of the remaining part of the rectangle?
\( 4\,\mathrm{cm}^2 \)
\( 2\,\mathrm{cm}^2 \)
\( 16\,\mathrm{cm}^2 \)
\( 1\,\mathrm{cm}^2 \)

1003158901

Level: 
C
An object is moving with a constant deceleration in a straight line. Displacement \( s \) (in metres) in time \( t \) (in seconds) is modelled by \( s=24t-3t^2 \). Find the displacement of the object from the moment it starts to decelerate until it stops.
\( 48\,\mathrm{m} \)
\( 144\,\mathrm{m} \)
\( 16\,\mathrm{m} \)
\( 96\,\mathrm{m} \)

1103120009

Level: 
C
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 \[ f(x)=-(x-a)^2+b\ \text{ and }\ g(x)=-(x-c)^2+d, \] where \( a \), \( b \), \( c \), \( d\in\mathbb{R} \). Following statements describe the relations between the pairs of the coefficients \( a \), \( b \), \( c \) and \( d \). Choose the true statement.
\( a=c-1\wedge b=d+4 \)
\( a=c+1\wedge b=d-4 \)
\( a=c-4\wedge b=d+1 \)
\( a=c+4\wedge b=d-1 \)

1103120007

Level: 
B
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: 
B
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: 
B
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 \( g(x)=\frac32(x+3)^2-2 \). 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: 
A
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 \( g \).
\( g(x) = x^2-3 \)
\( g(x) = (x+3)^2 \)
\( g(x) = x^2+3 \)
\( g(x) = (x-3)^2 \)

1103120003

Level: 
B
In the picture A, we are given the graph of the quadratic function \( f(x)=-2x^2 \). Use the graph of \( f \) as help to identify which of the graphs given in the picture B is the graph of \( g(x)=-2(x+4)^2 \). Choose what is the colour of the graph of \( g \). (Note: The graphs in the picture B were obtained by shifting the graph of \( f \).)
red
blue
green
yellow