2010017002
Level:
B
The graph of the function \(f(x) = x^{2} + 4x + 7\) is a parabola. Which of the following points is the vertex of this parabola?
\([-2;3]\)
\([3;-2]\)
\([0;7]\)
\([1;12]\)
Quadratic functions
2010017001
Level:
B
The graph of the function \(f(x) = -4x^{2} + 2\) is a parabola. Which of the following points is the vertex of this parabola?
\([0;2]\)
\(\left[\frac{\sqrt2}2;0\right]\)
\([2;0]\)
\([1;-2]\)
2010012304
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 \( g \).
\( g(x) = -x^2+2 \)
\( g(x) = (x-2)^2 \)
\( g(x) = -x^2-2 \)
\( g(x) = (x+2)^2 \)
2010012303
Level:
A
Find the \(y\)-intercept
of the following function. \[f(x) = 6x^{2} +12x - 7.2\]
\([0;-7.2]\)
\([-7.2;0]\)
\([6;0]\)
There is no \(y\)-intercept.
2010012302
Level:
A
Find the intervals of monotonicity of the quadratic function
\(f(x) = -3x^{2} + 2\).
The function is increasing on \( (- \infty ;0 ] \)
and decreasing on \( [ 0;\infty ) \).
The function is increasing on \((-\infty;2) \)
and decreasing on \( ( 2;\infty) \).
The function is increasing on \(\left(-\infty;\frac23 \right] \)
and decreasing on \( \left[ \frac23;\infty\right) \).
The function is decreasing on its domain.
2010012301
Level:
A
Find the \(x\)-intercepts
of the function \(f(x)= 2x^{2} + 2x - 12\).
\([-3;0]\) and
\([2;0]\)
\([0;-12]\) and
\([2;0]\)
\([-3;2]\) and
\([-3;-2]\)
The function \(f\) does
not have \(x\)-intercepts.
2010012205
Level:
C
Find all the values of the real parameter \( p \) such that \( f(x)=-2(x+3)^2+p \) is nonpositive for all \( x\in\mathbb{R} \).
\( p\in(-\infty;0] \)
\( p\in [ 0;\infty) \)
\( p\in(-\infty;-3] \)
\( p\in [ -3;\infty) \)
2010012204
Level:
C
Find all the values of the real parameter \( m \) such that \( f(x)=-2(x-m)^2-5\) is decreasing on \( (0;\infty) \).
\( m\in(-\infty;0] \)
\( m\in [0;\infty) \)
\( m\in(-\infty;-5] \)
\( m\in(-\infty;5] \)
2010012203
Level:
C
Find all the values of the real parameter \( m \) such that \( f(x)=3(x+m)^2-2\) is an even function.
\( m=0 \)
\( m>0 \)
\( m=-2 \)
\( m=2 \)
2010012202
Level:
A
Find all the values of the real parameter \( a \) such that \( f(x)=ax^2+2 \) is increasing on \( (0;\infty) \).
\( a\in(0;+\infty) \)
\( a\in(-\infty;0) \)
\( a\in [ 2;+\infty) \)
\( a\in(-\infty;2 ] \)