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anonymous

  • one year ago

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)

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  1. anonymous
    • one year ago
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    @assatmath

  2. anonymous
    • one year ago
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    help please

  3. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle f(x)=5x^2+10x+8 }\) 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 ?

  4. anonymous
    • one year ago
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    1

  5. anonymous
    • one year ago
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    b/2squared right?

  6. SolomonZelman
    • one year ago
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    yes, 1 is the number you need added. And now I will use a technique to which I refer to as a magic zero.

  7. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x)+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{-1})+8 }\)

  8. SolomonZelman
    • one year ago
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    then, take the negative one (which I labelled in red) out of the parenthesis, by expanding.

  9. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1}\color{red}{-1})+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+5(\color{red}{-1})+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})-5+8 }\) \(\large\color{black}{ \displaystyle f(x)=5(x^2+2x\color{blue}{+1})+3 }\)

  10. SolomonZelman
    • one year ago
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    Now, you need to do the very last step

  11. anonymous
    • one year ago
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    5(x+1)^2+3?

  12. anonymous
    • one year ago
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    answer choice D?

  13. SolomonZelman
    • one year ago
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    yes

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