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 \( x\in\mathbb{R} \).
\( p\in(-\infty;0] \)
\( p\in [ 0;\infty) \)
\( p\in(-\infty;-3] \)
\( p\in [ -3;\infty) \)
Quadratic functions
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 \( (0;\infty) \).
\( a\in(0;+\infty) \)
\( a\in(-\infty;0) \)
\( a\in [ 2;+\infty) \)
\( a\in(-\infty;2 ] \)
2010012201
Level:
C
Function \( f \) is given completely by the graph. Identify which of the following statements is true.
\( f(x)=-\left|x^2-4\right|;\ x\in[ -3;3] \)
\( f(x)=-\left|x^2+4\right|;\ x\in[ -3;3]\)
\( f(x)=-\left|x^2\right|-4;\ x\in[ -3;3]\)
\( f(x)=\left|-x^2\right|-4;\ x\in[ -3;3] \)
2000004311
Level:
C
The function \(f\) is graphed in the picture. Which of the following is its equation?
\( f(x) = \left|x^2-1\right|-1\)
\( f(x) = \left|x^2+1\right|-1\)
\( f(x) = \left|x^2+1\right|+1\)
\( f(x) = \left|x^2-1\right|+1\)
2000004310
Level:
C
The function \(f\) is graphed in the picture. Which of the following is its equation?
\( f(x) = x^2-4|x|\)
\( f(x) = \left|x^2-4x\right|\)
\( f(x) = \left|x^2\right|-4x\)
\( f(x) = \left|x^2\right|+4x\)
2000004309
Level:
C
The function \(f\) is graphed in the picture. Which of the following is its equation?
\( f(x) =- \left|x^2-4\right|\)
\( f(x) = -\left|x^2+4\right|\)
\( f(x) = -\left|x^2\right|-4\)
\( f(x) = -\left|x^2\right|+4\)
2000004308
Level:
C
The function \(f\) is graphed in the picture. Which of the following is its equation?
\( f(x) = \left|x^2-4x\right|\)
\( f(x) = \left|x^2+4x\right|\)
\( f(x) = \left|x^2\right|-4x\)
\( f(x) = \left|x^2\right|+4x\)
2000004307
Level:
C
The function \(f\) is graphed in the picture. Which of the following is its equation?
\(f(x) = \left|x^2-4\right|\)
\(f(x) = \left|x^2+4\right|\)
\(f(x) = \left|x^2-2\right|\)
\(f(x) = \left|x^2\right|+4\)