anonymous
  • anonymous
PLEAE HELP I GIVE ANYTHING Using the completing-the-square 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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
@assatmath
anonymous
  • anonymous
help please
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle f(x)=5x^2+10x+8 }\) 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 ?

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anonymous
  • anonymous
1
anonymous
  • anonymous
b/2squared right?
SolomonZelman
  • SolomonZelman
yes, 1 is the number you need added. And now I will use a technique to which I refer to as a magic zero.
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x)+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{-1})+8 }\)
SolomonZelman
  • SolomonZelman
then, take the negative one (which I labelled in red) out of the parenthesis, by expanding.
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{-1})+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+5(\color{red}{-1})+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})-5+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+3 }\)
SolomonZelman
  • SolomonZelman
Now, you need to do the very last step
anonymous
  • anonymous
5(x+1)^2+3?
anonymous
  • anonymous
answer choice D?
SolomonZelman
  • SolomonZelman
yes

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