Quadratic functions

1103120004

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 \( g \).
\( g(x) = x^2-3 \)
\( g(x) = (x+3)^2 \)
\( g(x) = x^2+3 \)
\( g(x) = (x-3)^2 \)

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 \( [ 4 ; +\infty)\).

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.

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 \( g \).
\( g(x) = -x^2+2 \)
\( g(x) = (x-2)^2 \)
\( g(x) = -x^2-2 \)
\( g(x) = (x+2)^2 \)