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.
9000014810
Level:
A
Find the domain and range of the quadratic function
\(f\)
graphed in the picture.
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left (-\infty ;2\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) =\mathbb{R} &
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2;\infty \right )
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left [ 0;\infty \right )&
\\&\mathop{\mathrm{Ran}}(f) = \left [ 2;4\right ]
\\ \end{aligned}\)
\(\begin{aligned}[t] &\mathop{\mathrm{Dom}}(f) = \left (-\infty ;0\right ] &
\\&\mathop{\mathrm{Ran}}(f) =\mathbb{R}
\\ \end{aligned}\)
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
1003083113
Level:
B
Determine the coordinates of the parabola vertex, if the parabola is the graph of \( f(x)=-\frac43 x^2+8x-13 \).
\( [3;-1] \)
\( [3;-22] \)
\( [-3;-1] \)
\( [-3;22] \)
1003083114
Level:
B
The graph of the function \( f(x)=4x^2+16x+11 \) is a parabola. Which of the following points is the vertex of this parabola?
\( [-2;-5] \)
\( [-2;7] \)
\( [2;11] \)
\( [-2;11] \)
1003108301
Level:
B
The graph of the quadratic function \( f \) intersects the coordinate axes at the points \( [1;0] \), \( [4;0] \), \( [0;8] \). Find the function \( f \).
\( f(x)=2x^2-10x+8 \)
\( f(x)=x^2-5x+4 \)
\( f(x)=-2x^2+10x-8 \)
\( f(x)=2x^2+10x+8 \)
1003108302
Level:
B
The graph of the quadratic function \( f \) is a parabola with the vertex \( [2;5] \). The parabola intersects the \( y \)-axis at the point \( [0;3] \). Find the function \( f \).
\( f(x)=-\frac12(x-2)^2+5 \)
\( f(x)=-\frac12(x+2)^2+5 \)
\( f(x)=-2(x-2)^2+5 \)
\( f(x)=-2(x+2)^2+5 \)
1003108303
Level:
B
Maximum value of the quadratic function \( f \) is \( 2 \). The graph of \( f \) intersects the \( x \)-axis at the points \( [-1;0] \) and \( [3;0] \). Find the function \( f \).
\( f(x)=-\frac12x^2+x+\frac32 \)
\( f(x)=x^2-2x+3 \)
\( f(x)=x^2-2x-3 \)
\( f(x)=-\frac12x^2-x+\frac32 \)