1103034603
Level:
B
Given graphs of the functions \( f(x)=x^2-6x+8\) and \( g(x)=-2x+4 \), find the solution set of the following inequality.
\[ x^2-6x+8\geq-2x+4 \]
\( \mathbb{R} \)
\( (-\infty;2]\cup[4;\infty) \)
\( \{2\} \)
\( [2;4] \)
Quadratic functions
1103034602
Level:
B
Given graphs of the functions \( f(x)=x^2-6x+8\) and \( g(x)=2x+1 \), find the solution set of the following inequality.
\[ x^2-6x+8>2x+1 \]
\( (-\infty;1)\cup(7;\infty) \)
\( (1;7) \)
\( (-\infty;2)\cup(4;\infty) \)
\( (1;\infty) \)
1103034601
Level:
B
Given graphs of the functions \( f(x)=x^2-6x+8\) and \( g(x)=-x^2-2x+24 \), find the solution set of the following inequality.
\[ x^2-6x+8\leq-x^2-2x+24 \]
\( [-2;4] \)
\( [2;4] \)
\( [0;24] \)
\( [-6;4] \)
9000033707
Level:
C
Identify the inequality with a solution graphed in the picture.
\(|x(3 - x)| > 3 - x\)
\(|x(x - 3)| < x - 3\)
\(|3x - x^{2}| > x - 3\)
\(|x^{2} - 3x| < 3 - x\)
\(x^{2} - 3|x| > 3 - x\)
\(x^{2} - 3|x| < x - 3\)
9000025610
Level:
B
Identify a quadratic equation which is solved by a graphical method in the
picture.
\(x^{2} - 6x + 9 = 0\)
\(x^{2} + 9x - 3 = 0\)
\(x^{2} - 9x - 3 = 0\)
\(x^{2} + 6x + 9 = 0\)
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.
\[
x^{2} + x - 1 > -\frac{1}
{2}x
\]
\(\left (-\infty ;-2\right )\cup \left (\frac{1}
{2};\infty \right )\)
\(\left (-2; \frac{1}
{2}\right )\)
\(\left [ -2; \frac{1}
{2}\right ] \)
\(\left (-\infty ;-2\right ] \cup \left [ \frac{1}
{2};\infty \right )\)