Question 1161321
x-intercept is the value of x when y = 0.
f(t) = t^2.
set that equal to 0 to get t^2 = 0
take the square root of both sides of the equation to get t = plus or minus sqrt(0) = 0.
here's the graph of that equation.


<img src = "http://theo.x10hosting.com/2020/061804.jpg" >


g(t) = (t-8)^2
set that equal to 0 to get (t-8)^2 = 0
take the square root of both sides of the equation to get plus or minus (t-8) = 0
solve to t in (t-8) = 0 to get t = 8.
solve tot t in -(t-8) = 0 to get t = 8.
here's the graph of that equation.


<img src = "http://theo.x10hosting.com/2020/061805.jpg" >


here's the graph of both equations on the same graph.


<img src = "http://theo.x10hosting.com/2020/061806.jpg" >


in the graphs, y replaces f(t) and g(t) and x replaces t.


from the graph, you can see that y = (x-8)^2 is the same as y = x^2 except that it is shifter to the right 8 units.


therefore, g(t) = f(t-8).


f(t) = t^2
f(t-8) = (t-8)^2 = g(t)