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 -6. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answer 1

f(x) has only one x-intercept when x=0

g(x)=-x^2-6

g(x)=-(x^2+6) so g(x) will have no x-intercepts as its maximum value will be -6.

g(x) is f(x) reflected about the x axis and shifted downwards by 6 units.