SOLUTION: I have a question regarding completing the square. There is no graphing involved, I promise! A problem reads: Let f(x)=x^2-16x and g(x)=a-x. There are two values of "a" so th

Question 463973: I have a question regarding completing the square. There is no graphing involved, I promise!
A problem reads:
Let f(x)=x^2-16x and g(x)=a-x. There are two values of "a" so that the graph of f o g crosses the y-axis at 0. Find the two values.
Obviously you won't have to graph this. We just have to find where x=0. So we plug that into g(x), and the result is "a". Plugging that into f(x), we get a^2-16a. From there I'm lost, because I don't know how to complete the square. Little help here?
Thanks,
Jessica
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
"Crosses the y-axis at 0" implies that the graph of f(g(x)) goes through the point (0,0), in which x = 0 and f(x) = 0.

If we let x = 0 then f(g(0)) = a^2 - 16a, which we set to 0. You don't have to complete the square on this one; instead it is better to factor the left side:

a(a-16) = 0

a = 0 or 16.

If you have to complete the square, divide the "a" coefficient by 2 to get -8, then square it to get 64. In other words,

a^2 - 16a + 64 = 64

(a-8)^2 = 64

and go on from there.
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