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 -5. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answer 1

x^2 only touches the x axis when x=0 and it increases without bound on either side of 0.

-x^2-5 never touches the x axis reaching a maximum at (0,-5) and decreasing without bound on either side of 0

g(x) is f(x) inverted and moved down five units...

Answer 2

The equation y = x^2 is the simplest form of a quadratic equation, it has one solution and the vertex sits on the origin of the graph. The equation g(x) = -x^2 - 5 tells us to flip the equation so that it opens to the bottom and move it 5 places down. This equation has no real solutions.