1103083104
Level:
A
The quadratic function \( f \) is graphed in the picture. Which of the following is its equation?
\( f(x)=\frac23x^2-4x+4 \)
\( f(x)=x^2-6x+7 \)
\( f(x)=\frac13x^2-2x+1 \)
\( f(x)=x^2-2x+4 \)
Quadratic functions
1103083103
Level:
A
The quadratic function \( f \) is graphed in the picture. Which of the following is its equation?
\( f(x)=-x^2-2x+1 \)
\( f(x)=x^2+2x+1 \)
\( f(x)=-x^2+2x+1 \)
\( f(x)=-x^2-4x-5 \)
1103083102
Level:
A
The quadratic function \( f \) is graphed in the picture. Which of the following is its equation?
\( f(x)=\frac13(x-3)^2+1 \)
\( f(x)=4\cdot(x-3)^2+1 \)
\( f(x)=(x+3)^2+4 \)
\( f(x)=4\cdot(x+1)^2+3 \)
1103083101
Level:
A
The quadratic function \( f \) is graphed in the picture. Which of the following is its equation?
\( f(x)=-(x-1)^2+2 \)
\( f(x)=(x-1)^2+2 \)
\( f(x)=(x+1)^2+2 \)
\( f(x)=-(x+1)^2+2 \)
1103082702
Level:
C
Function \( f \) is given completely by the graph. Identify which of the following statements is true.
\( f(x)=\left|x^2-1\right|;\ x\in[-2;2] \)
\( f(x)=\left|x^2\right|-1;\ x\in[-2;2] \)
\( f(x)=-\left|x^2+1\right|;\ x\in[-2;2] \)
\( f(x)=\left|-x^2\right|+1;\ x\in[-2;2] \)
1103067809
Level:
C
Given the graphs of the functions \( f(x)=\frac12x^2-3 \) and \( g(x)=\frac12x \), find the solution set of the following equation.
\[ \left|\frac12 x^2-3\right|=\left|\frac12 x\right| \]
\( \{ -3; -2; 2; 3 \} \)
\( \{ -2; 3 \} \)
\( \{ 2; 3 \} \)
\( \left\{ -\sqrt6; -2; \sqrt6; 3 \right\} \)
1103067801
Level:
C
Given the graph of the function \( f(x)=x^2 + 2x - 4 \), find the solution set of the following equation.
\[ \left|x^2 + 2x - 4\right|= 4 \]
\( \{ -4; -2; 0 ; 2 \} \)
\( \{ -4; 2 \} \)
\( \{ -4; 0; 2 \} \)
\( \left\{ -1-\sqrt5;-1+ \sqrt5 \right\} \)
1103034706
Level:
B
Given graphs of the functions \( f(x)=-x^2-x+6 \) and \( g(x)=x^2-4x+4 \), find the solution set of the following equation.
\[ -x^2-x+6=0 \]
\( \{-3;2\} \)
\( \{-0.5;2\} \)
\( \{2\} \)
\( \{0;6.25\} \)
1103034705
Level:
B
Given graphs of the functions \( f(x)=-x^2-x+6 \) and \( g(x)=x^2-4x+4 \), find the solution set of the following equation.
\[ x^2-4x+4 = -x^2-x+6 \]
\( \{-0.5;2\} \)
\( \{2\} \)
\( \{-3;2\} \)
\( \{0;6.25\} \)
1103034704
Level:
B
Given graphs of the functions \( f(x)=-x^2+4\) and \( g(x)=x+2 \), find the solution set of the following equation.
\[ -x^2+4=x+2 \]
\( \{-2;1\} \)
\( \{0;3\} \)
\( \{-2;2\} \)
\( \{0;4\} \)