A family of quadratic functions is given:
For 
, write the function rule, zeros, maximum and draw a parabola that is a graph of the function 
.
For 
calculate the area of the region between the parabola and the chord that connects the threads and the right intersection of the parabola with the 
axis.
Calculate for which value of the parameter 
and the function will have an extreme value at 
.
For which value of the parameter is the line 
tangent to the graph of the function . Calculate the tangent.
, the function f has a maximum value at 
is tangent to the graph of the function at 
