Quadratic functions

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

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

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

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

2000004301

Level: 
A
Find the intervals of monotonicity of the quadratic function \( f(x)=4-3x^2\).
The function is increasing on \( (-\infty; 0 ]\) and decreasing on \( [ 0 ; +\infty)\).
The function is increasing on \( (-\infty; 4 ]\) and decreasing on \( [ 4 ; +\infty)\).
The function is decreasing on \( (-\infty; 0 ]\) and increasing on \( [ 0 ; +\infty)\).
The function is decreasing on \( (-\infty; 4 ]\) and increasing on \( [ 4 ; +\infty)\).