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

Answer:

0 and 2

Step-by-step 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

$x=\sqrt{7}\\x=-\sqrt{7}$

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.