Quadratic functions

1103083107

Level: 
B
The quadratic functions \( f \) and \( g \) that have the same vertex \( V \) are graphed in the picture. The graph of \( g \) is the reflection of the graph of \( f \) in the vertex \( V \). Also, both the graphs are symmetric across \( y \)-axis. Identify the true statement about \( f \) and \( g \).
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the quadratic term only.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the linear term only.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the absolute term only.
None of the statements above is true.

1103083109

Level: 
B
The graphs of the quadratic functions \( f \) and \( g \) are shown in the picture. The graph of \( g \) is the reflection of the graph of \( f \) about \( y \)-axis. Identify which of the following statements about \( f \) and \( g \) is true.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the linear term only.
The equations of \( f \) and \( g \) differ in the sign of the coefficient at the quadratic term only.
The equations of \( f \) and \( g \) differ in in the sign of the coefficient at the absolute term only.
None of the statements above is true.

1103120001

Level: 
B
In the picture A, we are given the graph of the quadratic function \( f(x)=\frac12x^2 \). Use the graph of \( f \) as help to identify which of the graphs given in the picture B is the graph of \( g(x) =\frac12 x^2-2 \). Choose what is the colour of the graph of \( g \). (Note: The graphs in the picture B were obtained by shifting the graph of \( f \).)
blue
green
red
yellow

1103120002

Level: 
B
Let \( f(x)=2x^2 \). Given the graph of the function \( f \) and the graph of a function \( g \) which was obtained as a right shift of the graph of \( f \) (see the picture), choose the function \( g \).
\( g(x) = 2(x-3)^2 \)
\( g(x) = 2(x+3)^2 \)
\( g(x) = 2x^2+3 \)
\( g(x) = 2x^2-3 \)

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

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

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

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 \( g \).
\( g(x) = (x+2)^2-4 \)
\( g(x) = (x-2)^2-4 \)
\( g(x)=(x-4)^2-2 \)
\( g(x) = (x-2)^2+4 \)