SOLUTION: Suppose that the x intercepts of the graph of y=(x) are -8 and 1. What are the x intercepts of the graph of y=(x+4)? Explain step by step line by line.

Algebra ->  Linear-equations -> SOLUTION: Suppose that the x intercepts of the graph of y=(x) are -8 and 1. What are the x intercepts of the graph of y=(x+4)? Explain step by step line by line.       Log On


   



Question 1139683: Suppose that the x intercepts of the graph of y=(x) are -8 and 1. What are the x intercepts of the graph of y=(x+4)? Explain step by step line by line.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose that the x intercepts of the graph of y=%28x%29 are -8 and 1. What are the x intercepts of the graph of y=%28x%2B4%29?

notice that the y+coordinate is always zero for the x+intercept and the x+coordinate is always zero for the y+intercept.
That is, the x+ intercept is the point (x,0).
if the graph of y=%28x%29 are -8 and 1, the points are (-8,0) and (1,0)

and, the x+intercepts of the graph of+y=%28x%2B4%29 will be where %28x%2B4%29=-8 and %28x%2B4%29=1
x%2B4=-8
x=-8-4
x=-12
and
x%2B4=1
x=1-4
x=-3
so, the x+intercepts of the graph of y=%28x%2B4%29 are+-12 and -3

or at the points (-12,0) and (-3,0)

or do it this way:, using zero product theorem
factors of the function f+%28+x+%29+are:
 
f+%28+x+%29+=+%28+x+%2B+8+%29+%28+x+-+1+%29...x - intercepts of this function are -+8 and 1
multiply to expand
f+%28+x+%29++=+x%5E2+%2B+7+x+-+8
now find f+%28+x+%2B+4+%29+
f+%28+x+%2B+4+%29+=%28x%2B4%29%5E2+%2B+7+%28x%2B4%29+-+8
=x%5E2+%2B+8+x%2B16%2B7x%2B28+-+8
=x%5E2+%2B15x%2B36..........factor completely
=x%5E2+%2B3x%2B12x%2B36
=%28x%5E2+%2B12x%29%2B%283x%2B36%29
=x%28x+%2B12%29%2B3%28x%2B12%29
=%28x+%2B+12%29+%28x+%2B+3%29
so, the x - intercepts of the graph f+%28+x+%2B+2+%29 are -+12 and -3