Question

HELP ME PLEASE!!!!!
In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).In two or more complete sentences, compare the number of x-intercepts in the graph of f(t) = t2 to the number of x-intercepts in the graph of g(t) = (t – 8)2. Be sure to include the transformations that occurred between the parent function f(t) and its image g(t).

Answer 1

These are both parabolas, f(x) is the parent and g(x) is translated. f(x) is centered at the origin with one x-intercept. g(x) has the vertex shifted 8 units to the right from the origin along the x-axis.  Both of them have only one x-intercept; f(x)'s is at x=0, and g(x)'s is at x=8

Answer 2

The number of x-intercepts in the graph of f(t) is one and is equal to the number of x-intercepts in the graph of g(t)

we have

$f(t)=t^{2}$

This is a vertical parabola open upward

The vertex is the point $(0,0)$ and has one x-intercept

$g(t)=(t-8)^{2}$

This is also a vertical parabola open upward

The vertex is the point $(8,0)$ and has one x-intercept

The rule of the translation is

$(x,y)-----> (x+8,y)$

That means-----> the translation is $8$ units to the right

The number of x-intercepts in the graph of f(t) is one and is equal to the number of x-intercepts in the graph of g(t)