Question 1151375
Suppose that the​ x-intercepts of the graph of {{{y= f(x)}}} are {{{3}}} and {{{5}}}.
What are the​ x-intercepts of the graph of {{{y= f(x+8)}}}?

first note that {{{3}}} and {{{5}}} are roots:
{{{x[1]=3}}}
{{{x[2]=5}}}

so, use the Zero Product rule to find equation {{{y=f(x)}}} : 

{{{y=f ( x ) = ( x - x[1] ) ( x - x[2] )}}}

 {{{y=f ( x )= ( x - 3 ) ( x - 5)}}}

 {{{y=f ( x )=x^2 - 8 x + 15}}}=> x-intercepts of this function are {{{ 3}}} and {{{5}}}

see the graph:

{{{drawing( 600, 600, -10, 10, -10, 10,
locate(4,5,f( x )=x^2 - 8 x + 15),
 graph( 600, 600, -10, 10, -10, 10, x^2-8x+15)) }}}


then, 
{{{y=f ( x + 8 ) = (x+8)^2 - 8 (x+8) + 15}}}

{{{y=f ( x + 8 ) = x^2+16x+64 - 8x-64 + 15}}}

{{{y=f ( x + 8 ) = x^2+8x +15}}}...factor

{{{y=f ( x + 8 ) = (x + 3) (x + 5) }}}=> {{{(x + 3) (x + 5)=0 }}} if {{{x=-3}}} and {{{x=-5}}}


see the graph:

{{{drawing( 600, 600, -10, 10, -10, 10,
locate(-5,5,f( x+8 )=x^2+8x +15),
 graph( 600, 600, -10, 10, -10, 10, x^2+8x +15)) }}}


Answer : the x - intercepts of the graph {{{y=f ( x + 8 ) }}}are {{{- 3}}} and {{{-5}}}.