# Changing a Coefficient - Task

This figure shows the graph of function . Changing one of the coefficients of the the function f(x), modify this function in order to obtain functions with the properties listed below. In each case, check the following: Can the requested property be achieved by changing the coefficient of ? of x? the free coefficient? If possible' do it. If not' explain why.
1. The graph of the modified function passes through the origin of the coordinate system.
2. The graph of the modified function intersects the graph of the original function in one point only.
3. The graph of the modified function intersects the graph of the original function in more than one point.
4. The graph of the modified function does not intersect the graph of the original function.
5. The graph of the modified function does not intersect the x-axis.
6. The graph of the modified function intersects the x-axis in precisely one point.
7. The modified function has a minimum.
8. The axis of symmetry of the modified function is x=2.