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
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
ninguna respuesta está correcta
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.
\[
x^{2} + x - 1 > -\frac{1}
{2}x
\]
\(\left (-\infty ,-2\right )\cup \left (\frac{1}
{2},\infty \right )\)
\(\left (-2, \frac{1}
{2}\right )\)
\(\left [ -2, \frac{1}
{2}\right ] \)
\(\left (-\infty ,-2\right ] \cup \left [ \frac{1}
{2},\infty \right )\)
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?
\([2,9]\)
\([-2,13]\)
\([-4,13]\)
\([0,13]\)
9000014807
Level:
A
Find the \(x\)-intercepts
of the function \(f(x)= 3x^{2} + 6x - 9\).
\([-3,0]\) and
\([1,0]\)
\([0,9]\) and
\([1,0]\)
\([-3,2]\) and
\([-3,-2]\)
The function \(f\) does
not have \(x\)-intercepts.
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.