SOLUTION: 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)?

Algebra ->  Graphs -> SOLUTION: 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)?      Log On


   



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)?

Found 3 solutions by MathLover1, MathTherapy, Alan3354:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that the​ x-intercepts of the graph of y=+f%28x%29 are 3 and 5.
What are the​ x-intercepts of the graph of y=+f%28x%2B8%29?
first note that 3 and 5 are roots:
x%5B1%5D=3
x%5B2%5D=5
so, use the Zero Product rule to find equation y=f%28x%29
y=f+%28+x+%29+=+%28+x+-+x%5B1%5D+%29+%28+x+-+x%5B2%5D+%29
y=f+%28+x+%29=+%28+x+-+3+%29+%28+x+-+5%29
y=f+%28+x+%29=x%5E2+-+8+x+%2B+15=> x-intercepts of this function are +3 and 5
see the graph:


then,
y=f+%28+x+%2B+8+%29+=+%28x%2B8%29%5E2+-+8+%28x%2B8%29+%2B+15
y=f+%28+x+%2B+8+%29+=+x%5E2%2B16x%2B64+-+8x-64+%2B+15
y=f+%28+x+%2B+8+%29+=+x%5E2%2B8x+%2B15...factor
y=f+%28+x+%2B+8+%29+=+%28x+%2B+3%29+%28x+%2B+5%29+=> %28x+%2B+3%29+%28x+%2B+5%29=0+ if x=-3 and x=-5

see the graph:


Answer : the x - intercepts of the graph y=f+%28+x+%2B+8+%29+are -+3 and -5.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

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)?
From f(x) to f(x + 8), the ENTIRE parabola will be SHIFTED 8 units to the LEFT, so roots (3 and 5), or x-intercepts (3, 0) and (5, 0) are SHIFTED HORIZONTALLY,
8 units to the left thus making the new roots, (3 - 8), or - 5, and (5 - 8), or - 3. The points can also be written as: (- 5, 0) and (- 3, 0).

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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)?
============
It's not specified that the function is a parabola, or that it's a 2nd order function.