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).

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08-11-2017
Mathematics

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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).

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altavistard altavistard · Answer 1 · 2017-11-08T21:29:34+01:00

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.).