SOLUTION: I know how to find increasing and decreasing but I am having trouble finding this one: f(x) = −2(x + 1)2 + 4 Increasing:? Decreasing:? Please explain your answ

Algebra ->  Graphs -> SOLUTION: I know how to find increasing and decreasing but I am having trouble finding this one: f(x) = −2(x + 1)2 + 4 Increasing:? Decreasing:? Please explain your answ      Log On


   

Question 993358: I know how to find increasing and decreasing but I am having trouble finding this one:
f(x) = −2(x + 1)2 + 4
Increasing:?

Decreasing:?
Please explain your answer so that I understand. Thank you!
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
This equation is in vertex form.
The vertex of the parabola is (-1,4).
Since the multiplier for the quadratic term is negative ,-2, the parabola opens downwards and the maximum value occurs at the vertex.
So for x values before the vertex the y values are increasing and for x values after the vertex, the y values are decreasing.
Increasing : x%3C-1
Decreasing : x%3E-1
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Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = −2(x + 1)^2 + 4
f(x) = -2(x^2+2x+1) + 4
f(x) = -2x^2-4x+2
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graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2x%5E2-4x%2B2%29
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Take the derivative to get:
f'(x) = -4x-4
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Increasing:?
Solve: -4x-4 > 0
-4x > 4
x < -1
Increasing on (-oo,-1)
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Decreasing:?
Solve: -4x-4 < 0
-4x < 4
x > -1
Decreasing on (-1,+oo)
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Cheers,
Stan H.