anonymous
  • anonymous
Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 1 - (x - 6)^2 How would I solve this.
Mathematics
katieb
  • katieb
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misty1212
  • misty1212
HI!!
misty1212
  • misty1212
do you recognize it as a parabola?
anonymous
  • anonymous
Hello, again.

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anonymous
  • anonymous
Yes.
misty1212
  • misty1212
open up or down??
anonymous
  • anonymous
Up
misty1212
  • misty1212
hmmm
misty1212
  • misty1212
\[f(x)=-(x-6)^2+1\]
anonymous
  • anonymous
Oops, that's not what I graphed.
misty1212
  • misty1212
try it you will see it opens down because the leading coefficient it negative
anonymous
  • anonymous
Yes, I forgot about the negative.
anonymous
  • anonymous
Alright, I have graphed it.
misty1212
  • misty1212
you can see that it has a maximum when x = 6 it is increasing from \(-\infty\) to \(6\) and decreasing after that
anonymous
  • anonymous
So, increasing x<6, decreasing x>6
misty1212
  • misty1212
yes
anonymous
  • anonymous
Thank you, Misty. You're very helpful.

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