Quadratic functions

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 \( g \).
\( g(x) = 2(x-3)^2 \)
\( g(x) = 2(x+3)^2 \)
\( g(x) = 2x^2+3 \)
\( g(x) = 2x^2-3 \)

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

1003083110

Level: 
C
The graphs of the quadratic functions \( f \) and \( g \) have not the same vertex and \( f(x)=ax^2+bx+c \), where \( a \), \( b \), \( c \) are nonzero real numbers. Find \( g(x) \) such that the graph of \( g \) is the reflection of the graph of \( f \) about \( y \)-axis.
\( g(x)=ax^2-bx+c \), i.e. the equation of \( f \) and \( g \) differ in the sign of the coefficient at the linear term only
\( g(x)=-ax^2+bx+c \), i.e the equation of \( f \) and \( g \) differ in the sign of the coefficient at the quadratic term only
\( g(x)=ax^2+bx-c \), i.e. the equation of \( f \) and \( g \) differ in the sign of the coefficient at the absolute term only
\( g(x)=-ax^2-bx-c \), i.e. \( g(x)=-f(x) \)
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.