PRoblems with precalc functions

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The discussion revolves around finding the intervals of increase and decrease for the function f(x) = -x^2 - 6x - 8. The vertex was initially miscalculated as (3, -17) but was corrected to (-3, 1) after realizing the leading coefficient is -1, indicating the function opens downwards. The vertex marks the transition point between increasing and decreasing behavior. Additionally, a user attempted to ask a separate question about solving cos(theta) = 1/(√2) but was advised to start a new thread instead. The conversation highlights the importance of accurately determining function characteristics in precalculus.
crazy_shoes
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I'm trying to find where this function increases and decreases:

f(x) = = - x^2 - 6x - 8


I can get the vertex (h, k), which works out [by my math] to be (3, -17).

I'm just not sure where to go from here to get information like:
point of increase and decrease
domain and range

Thanks for any help!
 
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For the vertex, I get (-3,1), using the formula for h=-b/(2a). The vertex is where it switches from increasing to decreasing or from decreasing to increasing. The leading coefficient tells you which of these two cases it actually is...
 
Aaah... I see what I did wrong, I simply forgot that a=-1, I was thinking a=1.

When I set a to -1 instead of 1 it all works out! Thanks!
 
hi,
i need help finding 2 solutions to an equation. cos(theta) = 1/(sq.root of 2)
thanks !
 
Ramzi said:
hi,
i need help finding 2 solutions to an equation. cos(theta) = 1/(sq.root of 2)
thanks !

It's considered bad form to "hijack" an existing thread with a new question.

You should start a new thread.
 
im sorry ! its my first time using forums and all that stuff. my bad, but can anyone help me ?
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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