Quadratic functions

1003108306

Level: 
B
The \( x \)-axis is the tangent line of the graph of the quadratic function \( f \). The point of tangency has the coordinates \( [-2;0] \). Given \( f(-1)=-4 \), find the function \( f \).
\( f(x)=-4x^2-16x-16 \)
\( f(x)=-4x^2-16x+16 \)
\( f(x)=-\frac49x^2+\frac{16}9x-\frac{16}9 \)
\( f(x)=4x^2-16x+16 \)

1003108308

Level: 
B
Which of the following information are insufficient to determine quadratic function uniquely?
two intersection points with the \( x \)-axis and \( x \)-coordinate of the vertex
two intersection points with the \( x \)-axis and \( y \)-coordinate of the vertex
two intersection points with the \( x \)-axis and any other point of the function
coordinates of the vertex and the intersection with the \( y \)-axis

1003108309

Level: 
B
The graph of the quadratic function \( f \) intersects coordinate axes at the points \( [-3;0] \), \( [1;0] \), \( \left[0;\frac32\right] \). Find the function \( f \).
\( f(x)=-\frac12(x+1)^2+2 \)
\( f(x)=-\frac12(x+1)^2+\frac12 \)
\( f(x)=-\frac12(x-1)^2+2 \)
\( f(x)=\frac12(x-1)^2+2 \)

1003108310

Level: 
B
The graph of the quadratic function \( f \) has the vertex at the point \( [3; -1] \) and it passes through the point \( [ -1; 3] \). Find the function \( f \).
\( f(x)=\frac14x^2-\frac32x+\frac54 \)
\( f(x)=\frac14x^2+\frac32x+\frac54 \)
\( f(x)=-\frac14x^2+\frac32x-\frac{13}4 \)
\( f(x)=x^2+6x+8 \)