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anonymous

  • one year ago

If g(x) = 2x2 + bx + 5 and g(1) = 4, what is the value of g(-1)? 1 2 3 7 10

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  1. anonymous
    • one year ago
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    @SolomonZelman

  2. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle g(x)=2x^2+bx+5 }\) correct?

  3. anonymous
    • one year ago
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    yes sir

  4. SolomonZelman
    • one year ago
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    Your given that \(\large\color{red}{ \color{black}{g(}1\color{black}{)=}\color{blue}{4} }\), so lets apply this. \(\large\color{black}{ \displaystyle g(x)=2x^2+bx+5 }\) for any function g(x)=function with x's. when you do g(1), every single x is replaced by a 1. This gets us: \(\large\color{black}{ \displaystyle g(\color{red}{1})=2(\color{red}{1})^2+b(\color{red}{1})+5 }\)

  5. SolomonZelman
    • one year ago
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    Now, we know that \(\large\color{red}{ \color{black}{g(}1\color{black}{)=}\color{blue}{4} }\) So, we can substitute 4 instead of g(1), the following way: \(\large\color{black}{ \displaystyle \color{blue}{4}=2(\color{red}{1})^2+b(\color{red}{1})+5 }\)

  6. SolomonZelman
    • one year ago
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    All you need to do know is to simplify and solve for b:)

  7. anonymous
    • one year ago
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    i still need help sir solving for b @SolomonZelman

  8. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \color{blue}{4}=2(\color{red}{1})^2+b(\color{red}{1})+5 }\) ok, what is `2(1)²` equal to?

  9. anonymous
    • one year ago
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    2?

  10. SolomonZelman
    • one year ago
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    yes

  11. SolomonZelman
    • one year ago
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    So lets write that \(\large\color{black}{ \displaystyle \color{blue}{4}=2+b(\color{red}{1})+5 }\)

  12. SolomonZelman
    • one year ago
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    b(1) is b•1, and that is just b. Right?

  13. anonymous
    • one year ago
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    yes

  14. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \color{blue}{4}=2+b+5 }\)

  15. SolomonZelman
    • one year ago
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    can you solve this, or need a little more help?

  16. anonymous
    • one year ago
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    i need a little more help please

  17. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \color{blue}{4}=2+b+5 }\) \(\large\color{black}{ \displaystyle \color{blue}{4}=7+b }\)

  18. SolomonZelman
    • one year ago
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    agree?

  19. anonymous
    • one year ago
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    but do we not consider the b to be a imaginary 1 ?

  20. SolomonZelman
    • one year ago
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    lol, it seems as though you are having a bad day right now...

  21. SolomonZelman
    • one year ago
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    4=7+b ust subtract 7 from both sides

  22. anonymous
    • one year ago
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    lol no sir i just want to understand it fully

  23. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle 4=7+b }\) \(\large\color{black}{ \displaystyle 4\color{magenta}{-7}=7+b \color{magenta}{-7} }\) \(\large\color{black}{ \displaystyle 4\color{magenta}{-7}=\cancel{7}+b \cancel{\color{magenta}{-7}} }\)

  24. SolomonZelman
    • one year ago
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    b=?

  25. anonymous
    • one year ago
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    3

  26. SolomonZelman
    • one year ago
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    not exactly, but close...

  27. SolomonZelman
    • one year ago
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    b can be negative too:)

  28. anonymous
    • one year ago
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    but my answer choices are not negative

  29. SolomonZelman
    • one year ago
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    then they are wrong, because the answer is -3.

  30. SolomonZelman
    • one year ago
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    Oh, we are not done yet....

  31. SolomonZelman
    • one year ago
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    the answer choices are for g(-1)

  32. SolomonZelman
    • one year ago
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    and -3 that we found just now is the value of b

  33. anonymous
    • one year ago
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    yes

  34. SolomonZelman
    • one year ago
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    Now we know our function entirely. g(x) = 2x² - 3x + 5

  35. SolomonZelman
    • one year ago
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    And now find g(-1), by plugging -1 instead of x.

  36. SolomonZelman
    • one year ago
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    g(x) = 2x² - 3x + 5 g(-1) = 2(-1)² - 3(-1) + 5=?

  37. anonymous
    • one year ago
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    g(-1)=2 -3+5=4

  38. anonymous
    • one year ago
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    ???

  39. anonymous
    • one year ago
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    or is it 10?

  40. SolomonZelman
    • one year ago
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    oh wait

  41. anonymous
    • one year ago
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    i think it is 10 sir

  42. SolomonZelman
    • one year ago
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    g(-1) = 2(-1)² - 3(-1) + 5 g(-1) = 2 - - 3 + 5 g(-1) = 2 + 3 + 5 g(-1) = 10

  43. SolomonZelman
    • one year ago
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    correct

  44. anonymous
    • one year ago
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    thank you so much you are awesome :)

  45. SolomonZelman
    • one year ago
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    You are welcome!

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