1003083114
Level:
B
The graph of the function \( f(x)=4x^2+16x+11 \) is a parabola. Which of the following points is the vertex of this parabola?
\( [-2;-5] \)
\( [-2;7] \)
\( [2;11] \)
\( [-2;11] \)
Quadratic functions
1003083113
Level:
B
Determine the coordinates of the parabola vertex, if the parabola is the graph of \( f(x)=-\frac43 x^2+8x-13 \).
\( [3;-1] \)
\( [3;-22] \)
\( [-3;-1] \)
\( [-3;22] \)
1103083112
Level:
A
Find the graph of the quadratic function \( f(x)=\frac15x^2-2x+6 \).
1103083111
Level:
A
Find the graph of the quadratic function \( f(x)=2x^2+12x+16 \).
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.
1003083108
Level:
C
The parabolas of the functions \( f \) and \( g \) have the same vertex \( V \) and \( f(x)=ax^2+c \), where \( a \) and \( c \) are nonzero real numbers. Find \( g(x) \) such that the graphs of \( f \) and \( g \) are symmetric about the vertex \( V \) and that \( y \)-axis is their line of symmetry.
\( g(x)=-ax^2+c\), i.e. the equations of \( f \) and \( g \) differ in the sign of the coefficient at the quadratic term only
\( g(x)=ax^2-c\), i.e. the equations of \( f \) and \( g \) differ in the sign of the coefficient at the linear term only
\( g(x)=-ax^2-c \), i.e. \( g(x)=-f(x) \)
None of the statements above is true.
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.
1103083106
Level:
A
The quadratic function \( f \) is graphed in the picture. Which of the following is its equation?
\( f(x)=x^2+6x+9 \)
\( f(x)=x^2-6x+9 \)
\( f(x)=x^2-3 \)
\( f(x)=x^2+3 \)
1103083105
Level:
A
The quadratic function \( f \) is graphed in the picture. Which of the following is its equation?
\( f(x)=-2x^2-4x-5 \)
\( f(x)=-2x^2+12x-19 \)
\( f(x)=-x^2-2x-4 \)
\( f(x)=x^2-2x-5 \)