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 -7. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answer 1

The equation to this graph is f(x) = x² which is a quadratic function. The vertex is at the origin (0,0). This equation only has 1 x-intercept.

The graph is then transformed forming the equation, g(x) = x² - 7, which vertically shifts 7 units down. This equation has 2 x-intercepts.

Answer 2

The graph has an equation f(x) = x² which is a quadratic function with the vertex at the origin and it has only one x-intercept.

The graph is transformed into g(x) = x² - 7 which is a vertical shift 7 units downward. It has 2 x-intercepts.