Does the graph of f(x)=ax^2+bx+c have 2 intersections with axis-x? (1)

(ax^2+bx+c) graph is a parabola which could look like any of these:


It may intersect x axis in 2 points/1 point of no point. Where it is placed on the co-ordinate depends on the values of the coefficients.

(1) f(x+2) have 2 intersections with axis-x.

The graph of f(x+2) is 2 units to the left of graph of f(x). The graph is exactly the same except it moves 2 units to the left. For example:


So if f(x + 2) has 2 points of intersection, so will f(x). It will be the same graph 2 units to the right of graph of f(x +2).
Hence this statement alone is sufficient.

(2) f(x)+2 have 2 intersections with axis-x.
f(x) + 2 will be 2 units above the graph of f(x). It is possible that f(x) has two points of intersection too but it is possible that f(x) + 2 is graph B shown in pic above while f(x) is graph A. Hence f(x) may have no point of intersection or 1 point of intersection.
This alone is not sufficient.

Answer (A)