1103083112
Level:
A
Find the graph of the quadratic function \( f(x)=\frac15x^2-2x+6 \).
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 \( [ 4 ; +\infty)\).
2010012202
Level:
A
Find all the values of the real parameter \( a \) such that \( f(x)=ax^2+2 \) is increasing on \( (0;\infty) \).
\( a\in(0;+\infty) \)
\( a\in(-\infty;0) \)
\( a\in [ 2;+\infty) \)
\( a\in(-\infty;2 ] \)
2010012301
Level:
A
Find the \(x\)-intercepts
of the function \(f(x)= 2x^{2} + 2x - 12\).
\([-3;0]\) and
\([2;0]\)
\([0;-12]\) and
\([2;0]\)
\([-3;2]\) and
\([-3;-2]\)
The function \(f\) does
not have \(x\)-intercepts.
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.
2010012303
Level:
A
Find the \(y\)-intercept
of the following function. \[f(x) = 6x^{2} +12x - 7.2\]
\([0;-7.2]\)
\([-7.2;0]\)
\([6;0]\)
There is no \(y\)-intercept.
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 \( g \).
\( g(x) = -x^2+2 \)
\( g(x) = (x-2)^2 \)
\( g(x) = -x^2-2 \)
\( g(x) = (x+2)^2 \)
9000014801
Level:
A
Identify a point which is on the graph of the function
\(f(x) = 3x^{2} + 3x - 2\).
\(B = [2;16]\)
\(A = [0;3]\)
\(C = [-1;0]\)
\(D = [5;-8]\)
9000014802
Level:
A
Let \(f(x) = -x^{2} + 11x - 2\).
Which of the following statements is true?
\(f(-2) = -28\)
\(f(0) = 2\)
\(f(3.5) = 12.25\)
\(f\left (\frac{1}
{2}\right ) = \frac{15}
{4} \)