Question

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) =x2 to the number of x-intercepts in the graph of g(x) = x2 +2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answer 1

Important:  Please use " ^ " to indicate exponentiation:

"f(x) =x^2 to the number of x-intercepts in the graph of g(x) = x^2 +2."

Notes:  the graph of f(x) = x^2 is a vertical parabola that opens up.  It has its vertex at (0,0).  This is the only point at which f(x)=x^2 has a horiz. intercept.

g(x) = x^2 + 2 has a graph that looks the same as that of f(x) = x^2, EXCEPT that the whole graph is moved 2 units UP.  This new graph never touches or intersects the x-axis.  Therefore, g(x) has NO horiz. intercepts (no x-int.).