Question

In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x^2 to the number of x-intercepts in the graph of g(x) = -x^2 -5. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
NEED HELP ASAP

Answer 1

The graph of f(x) = x^2 has only one x-intercept since its vertex is at the origin, (0,0) and it opens up. When comparing the graph of g(x) = -x^2 -5 with the graph of f(x) = x^2, g(x) is the graph of f(x) first reflected in the x-axis and then translated 5 units down. The graph of g(x) has no x-intercepts since its a parabola that opens downward (result of reflection in x-axis) and its vertex at (0,-5) is situated below the x-axis.