9000014805
Level:
B
Find the minimum value of the quadratic function
\(f(x)= 4x^{2} - 4x + 7\).
\(6\)
\(7\)
does not exist
\(- 4\)
Quadratic functions
9000014806
Level:
B
Find the maximum value of the quadratic function
\(f(x) = 0.02x^{2} - 7x + 4\).
does not exist
\(4\)
\(0.02\)
\(- 7\)
9000022306
Level:
B
Using the graph of the function \(f(x)= -x^{2} - 2x + 8\)
solve the following inequality.
\[
-x^{2} - 2x + 8\leq 5
\]
\(\left (-\infty ;-3\right ] \cup \left [ 1;\infty \right )\)
\(\left (-\infty ;-4\right ] \cup \left [ 2;\infty \right )\)
\(\left [ -3;1\right ] \)
\(\left [ -4;2\right ] \)
9000022307
Level:
B
Using the graph of the function \(f(x) = x^{2} - x - 6\)
solve the system of inequalities.
\[
-4 < x^{2} - x - 6 < 0
\]
\((-2;-1)\cup (2;3)\)
\((-2;3)\)
\((-\infty ;-2)\cup (3;\infty )\)
\((-\infty ;-1)\cup (2;\infty )\)
9000022308
Level:
B
Using graphs of the functions \(f(x)= -2x^{2} + 3x + 4\)
and \(g(x) = x\)
solve the following quadratic inequality.
\[
-2x^{2} + 3x + 4\geq x
\]
\(\left [ -1;2\right ] \)
\(\{ - 1;2\}\)
\(\left (-1;2\right )\)
\(\left (-\infty ;-1\right )\cup \left (2;\infty \right )\)
9000022309
Level:
B
Using graphs of the functions \(f(x) = x^{2} + x - 1\)
and \(g(x) = -\frac{1}
{2}x\)
solve the following quadratic inequality.
\[
x^{2} + x - 1 > -\frac{1}
{2}x
\]
\(\left (-\infty ;-2\right )\cup \left (\frac{1}
{2};\infty \right )\)
\(\left (-2; \frac{1}
{2}\right )\)
\(\left [ -2; \frac{1}
{2}\right ] \)
\(\left (-\infty ;-2\right ] \cup \left [ \frac{1}
{2};\infty \right )\)
9000025610
Level:
B
Identify a quadratic equation which is solved by a graphical method in the
picture.
\(x^{2} - 6x + 9 = 0\)
\(x^{2} + 9x - 3 = 0\)
\(x^{2} - 9x - 3 = 0\)
\(x^{2} + 6x + 9 = 0\)
9100025608
Level:
B
Identify the picture which shows solution of
\[
\text{$2x^{2} - 5x - 3 = 0$}
\]
by a graphical method.
9100033706
Level:
B
Identify a picture which shows graphical solution of the following quadratic
inequality, assuming that the solution is the red set.
\[
-x^{2} + x + 2 > 2x
\]
1003083108
Level:
C
The parabolas of the functions \( f \) and \( g \) have the same vertex \( V \) and \( f(x)=ax^2+c \), where \( a \) and \( c \) are nonzero real numbers. Find \( g(x) \) such that the graphs of \( f \) and \( g \) are symmetric about the vertex \( V \) and that \( y \)-axis is their line of symmetry.
\( g(x)=-ax^2+c\), i.e. the equations of \( f \) and \( g \) differ in the sign of the coefficient at the quadratic term only
\( g(x)=ax^2-c\), i.e. the equations of \( f \) and \( g \) differ in the sign of the coefficient at the linear term only
\( g(x)=-ax^2-c \), i.e. \( g(x)=-f(x) \)
None of the statements above is true.