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.
Quadratic functions
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?
\([2;9]\)
\([-2;13]\)
\([-4;13]\)
\([0;13]\)
9000014805
Level:
B
Find the minimum value of the quadratic function
\(f(x)= 4x^{2} - 4x + 7\).
\(6\)
\(7\)
does not exist
\(- 4\)
9000014806
Level:
B
Find the maximum value of the quadratic function
\(f(x) = 0.02x^{2} - 7x + 4\).
does not exist
\(4\)
\(0.02\)
\(- 7\)
9000014802
Level:
A
Let \(f(x) = -x^{2} + 11x - 2\).
Which of the following statements is true?
\(f(-2) = -28\)
\(f(0) = 2\)
\(f(3.5) = 12.25\)
\(f\left (\frac{1}
{2}\right ) = \frac{15}
{4} \)
9000014801
Level:
A
Identify a point which is on the graph of the function
\(f(x) = 3x^{2} + 3x - 2\).
\(B = [2;16]\)
\(A = [0;3]\)
\(C = [-1;0]\)
\(D = [5;-8]\)
9000014810
Level:
A
Find the domain and range of the quadratic function
\(f\)
graphed in the picture.
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left (-\infty ;2\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2;\infty \right )
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left [ 0;\infty \right )&
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2;4\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left (-\infty ;0\right ] &
\\&\mathop{\mathrm{Ran}}(f) =\mathbb{R}
\\ \end{aligned}\)