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

0 and 2

Explanation:

We know that the x intercept is the point where the graph intersect the x axis. At this point , the y coordinate is 0. Hence in order to find the x intercepts we have to put y = 0 and solve it for x .

`f(x)=x^2`

put f(x)=0

`x^2=0\\x=0`

`g(x)=x^2-7`

put g(x)=0

`x^2-7=0`

`x^2=7`

taking square root on both sides we get

`x=√(7)\\x=-√(7)`

hence in f(x) we have x intercept is one and in g(x) we have two x intercepts.

Part B:
`g(x) = x^2-7`

`f(x)=x^2`

Hence
`g(x)=f(x)-7`

Hence g(x) is pulled down vertically by 7 units and it will be our transformation.

Answer 2

The graph has an equation f(x) = x² which is a quadratic function with the vertex at the origin and an x-intercept of 0.
The graph is transformed into g(x) = x² - 7 which is a vertical shift 7 units downward resulting to an x-intercept of -7.