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anonymous

  • one year ago

I can't figure this one out.. MEDAL AND FAN FOR ANYONE WHO CAN UN-CONFUZZLE ME!! For the function f(x) = –(x + 1)2 + 4, identify the vertex, domain, and range.

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  1. Loser66
    • one year ago
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    Where are you stuck?

  2. anonymous
    • one year ago
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    mostly the vertex

  3. Loser66
    • one year ago
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    open parentheses, what do you have for f(x) ?

  4. anonymous
    • one year ago
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    f(x)=-x+1^2+4

  5. Loser66
    • one year ago
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    nnnnnnnnnnnnnope

  6. Loser66
    • one year ago
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    \(f(x) = -(x+1)^2 +4\) redo, please. Use Foil

  7. anonymous
    • one year ago
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    -x+5? after you simplify ?

  8. anonymous
    • one year ago
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    How do you find out the range aswell I vaguely remember

  9. Loser66
    • one year ago
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    \((x+1)^2 =(x+1)(x+1)\) ,using Foil to open parentheses

  10. anonymous
    • one year ago
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    Oh ya I forgot you had to do that with squared binomials

  11. anonymous
    • one year ago
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    X^2+2x+1

  12. Loser66
    • one year ago
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    Yup, don't forget, before them, you have - sign, after them you have +4 now, put all in, what do you get for f(x) ??

  13. anonymous
    • one year ago
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    Where did you get the +4 from?

  14. Loser66
    • one year ago
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    From the original problem.

  15. anonymous
    • one year ago
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    Oh ok, did I mess up the foil? You said something about a negative and when I plugged 4 into \[x ^{2}+2x+1 \] I got 25 and that's not one of the choices for the y-coordinate and it doesn't really make sense

  16. Loser66
    • one year ago
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    NOOOOOOOOOPe

  17. Loser66
    • one year ago
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    \(f(x) = \huge \color{red}{-} (x+1)^2 +4\\~~~~~~~~~~=\huge\color{red}{-} (x^2+2x+1)+4\\=\huge -x^2-2x-1+4\) ok??

  18. Loser66
    • one year ago
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    hey!!! YES or NO?

  19. anonymous
    • one year ago
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    OOHHH

  20. anonymous
    • one year ago
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    YES got it :) but how bought the range? Ik the domains gunna be all real numbers

  21. Loser66
    • one year ago
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    wait, simplify it, please.

  22. Loser66
    • one year ago
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    don't know??? why?? -1+4 =?

  23. anonymous
    • one year ago
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    3?

  24. Loser66
    • one year ago
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    yes, so that \(f(x) =-x^2-2x+3\) right?

  25. Loser66
    • one year ago
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    From this, the REAL process starts.

  26. Loser66
    • one year ago
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    what are a, b, c on it?

  27. Loser66
    • one year ago
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    a=? b=? c=?

  28. anonymous
    • one year ago
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    a=-1 b=-2 c=3

  29. Loser66
    • one year ago
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    yup, hence the vertex has x-coordinate is \(x= -b/2a\) , hence x =??

  30. anonymous
    • one year ago
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    x=4

  31. Loser66
    • one year ago
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    \(x=-\dfrac{b}{2a}=-\dfrac{-2}{2*(-1)}=??\)

  32. anonymous
    • one year ago
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    1

  33. anonymous
    • one year ago
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    so the vertex is 1,4?

  34. anonymous
    • one year ago
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    TY FOR HELPING ME FIGURE HAT PART OUT :)))) but how do I know what the range is going to be?

  35. Loser66
    • one year ago
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    to it, when you have vertex, and the parabola is downward, hence the range is from - infinitive to y-coordinate of the vertex.

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