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anonymous
 one year ago
PLEAE HELP I GIVE ANYTHING
Using the completingthesquare method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point.
Maximum at (1, 8)
Minimum at (1, 8)
Maximum at (–1, 3)
Minimum at (–1, 3)
anonymous
 one year ago
PLEAE HELP I GIVE ANYTHING Using the completingthesquare method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point. Maximum at (1, 8) Minimum at (1, 8) Maximum at (–1, 3) Minimum at (–1, 3)

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f(x)=5x^2+10x+8 }\) factor the 1st 2 terms out of 5, \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x)+8 }\) then, tell me what number would you want added into the parenthesis ?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, 1 is the number you need added. And now I will use a technique to which I refer to as a magic zero.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x)+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{1})+8 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1then, take the negative one (which I labelled in red) out of the parenthesis, by expanding.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{1})+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+5(\color{red}{1})+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})5+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+3 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Now, you need to do the very last step
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