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
ninguna respuesta está correcta
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 \( f \).
\( f(x)=-\frac12x^2+x+\frac32 \)
\( f(x)=x^2-2x+3 \)
\( f(x)=x^2-2x-3 \)
\( f(x)=-\frac12x^2-x+\frac32 \)