1103123809
Level:
B
Choose the equation of which the solution is graphed in the picture.
\( x^2-4x=0 \)
\( x^2-4=0 \)
\( x^2-2x=0 \)
\( x^2-2=0 \)
Quadratic functions
1103148604
Level:
B
The total mechanical energy \( E \) of an object is given by the formula \( E=mgh+\frac12mv^2 \), where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity (about \( 10\,\mathrm{m}/\mathrm{s}^2 \)), \( h \) is the height of the object above the ground and \( v \) is the velocity of that object. Suppose that an object of the fixed mass \( m \) moves horizontally in the constant height \( h \) above the ground. Choose the graph, which could represent the dependence between the total mechanical energy (\( E \)) and velocity (\( v \)) of the object.
2000004302
Level:
B
In the picture A, the graph of the quadratic function \( f(x) = x^2\) is shown. With the aid of the graph of \(f\) identify which of the graphs shown in the picture B is the graph of \( g(x) = -\frac{1}{2} x^2\). What is the color of the graph of \(g\)? (Note: Each graph in the picture B is the graph of some transformation of \(f\).)
green
blue
yellow
red
2000004303
Level:
B
In the picture A, the graph of the quadratic function \( f(x) = x^2\) is shown. With the aid of the graph of \(f\) identify which of the graphs shown in the picture B is the graph of \( g(x) = (x+2)^2\). What is the color of the graph of \(g\)? (Note: Each graph in the picture B was obtained by shifting the graph of \(f\).)
red
green
yellow
blue
2000004304
Level:
B
In the picture A, the graph of the quadratic function \( f(x) = x^2\) is shown. With the aid of the graph of \(f\) identify which of the graphs shown in the picture B is the graph of \( g(x) = (x-2)^2\). What is the color of the graph of \(g\)? (Note: Each graph in the picture B is the graph of some transformation of \(f\).)
yellow
red
green
blue
2000004305
Level:
B
In the picture A, the graph of the quadratic function \( f(x) = x^2\) is shown. With the aid of the graph of \(f\) identify which of the graphs shown in the picture B is the graph of \( g(x) = x^2-2x-3=(x+1)(x-3)\). What is the color of the graph of \(g\)? (Note: Each graph in the picture B was obtained by shifting the graph of \(f\).)
blue
red
yellow
green
2000004306
Level:
B
Let \(f(x) = x^2\). Given the graph of the function \(f\) and the graph of a function \(g\) (see the picture), choose the function \(g\).
\( g(x) =-x^2+4\)
\( g(x) =x^2-4\)
\( g(x) =x^2-2\)
\( g(x) =-x^2+2\)
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?
\([0;2]\)
\(\left[\frac{\sqrt2}2;0\right]\)
\([2;0]\)
\([1;-2]\)
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?
\([-2;3]\)
\([3;-2]\)
\([0;7]\)
\([1;12]\)
2010017003
Level:
B
Find the maximum value of the quadratic function
\(f(x)= -x^{2} +2x +1\).
\(2\)
\(1\)
The maximum value of the function \(f\) does not exist.
\(0\)