This figure shows the graph of function [math]f\left(x\right)=-2x^2+4x+5[/math].[br]Changing one of the coefficients of the the function f(x), modify this function in order to obtain functions with the properties listed below.[br]In each case, check the following: Can the requested property be achieved by changing the coefficient of [math]x^2[/math]? of x? the free coefficient?[br]If possible' do it. If not' explain why.[br] [br] [br]

[list=1][*]The graph of the modified function passes through the origin of the coordinate system. [/*][*]The graph of the modified function intersects the graph of the original function in one point only. [/*][*]The graph of the modified function intersects the graph of the original function in more than one point. [/*][*]The graph of the modified function does not intersect the graph of the original function. [/*][*]The graph of the modified function does not intersect the x-axis.[/*][*]The graph of the modified function intersects the x-axis in precisely one point. [/*][*]The modified function has a minimum.[br][/*][*]The axis of symmetry of the modified function is x=2.[/*][/list]