9000025610
Level:
B
Identify a quadratic equation which is solved by a graphical method in the
picture.
\(x^{2} - 6x + 9 = 0\)
\(x^{2} + 9x - 3 = 0\)
\(x^{2} - 9x - 3 = 0\)
\(x^{2} + 6x + 9 = 0\)
Quadratic Functions
9000022306
Level:
B
Using the graph of the function \(f(x)= -x^{2} - 2x + 8\)
solve the following inequality.
\[
-x^{2} - 2x + 8\leq 5
\]
\(\left (-\infty ;-3\right ] \cup \left [ 1;\infty \right )\)
\(\left (-\infty ;-4\right ] \cup \left [ 2;\infty \right )\)
\(\left [ -3;1\right ] \)
\(\left [ -4;2\right ] \)
9000022302
Level:
A
Complete the following statement, if possible: „The function \(f\colon y = -x^{2} - 2x + 15\) attains only
... values on the interval \([- 5;3] \).”
nonnegative
positive
negative
neither of the above is valid
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.
\[
x^{2} + x - 1 > -\frac{1}
{2}x
\]
\(\left (-\infty ;-2\right )\cup \left (\frac{1}
{2};\infty \right )\)
\(\left (-2; \frac{1}
{2}\right )\)
\(\left [ -2; \frac{1}
{2}\right ] \)
\(\left (-\infty ;-2\right ] \cup \left [ \frac{1}
{2};\infty \right )\)
9000014808
Level:
A
Find the intervals of monotonicity of the quadratic function
\(f(x) = 2x^{2} + 3\).
The function is increasing on \(\left [ 0;\infty \right )\)
and decreasing on \(\left (-\infty ;0\right ] \).
The function is increasing on \(\left (3;\infty \right )\)
and decreasing on \(\left (-\infty ;3\right )\).
The function is increasing on \(\left [ -\frac{3}
{2};\infty \right )\)
and decreasing on \(\left (-\infty ;-\frac{3}
{2}\right ] \).
The function is increasing on its domain.
9000014809
Level:
A
Find the \(y\)-intercept
of the following function: \[f(x) = 10x^{2} - 18x - 6.3\]
\([0;-6.3]\)
\([10;0]\)
\([0.3;0]\)
There is no \(y\)-intercept.
9000014803
Level:
B
The graph of the function \(f(x) = 6x^{2} + 3\) is a parabola. Which of the following points is the vertex of this parabola?
\([0;3]\)
\([3;0]\)
\([1;9]\)
\([1;2]\)
9000014804
Level:
B
The graph of the function \(f(x) = x^{2} - 4x + 13\) is a parabola. Which of the following points is the vertex of this parabola?
\([2;9]\)
\([-2;13]\)
\([-4;13]\)
\([0;13]\)