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anonymous

  • one year ago

y=-(x+2)(x-4) find the domian,range,axis of symmetry

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  1. anonymous
    • one year ago
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    @welshfella

  2. misty1212
    • one year ago
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    HI!!

  3. misty1212
    • one year ago
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    first step would be to multiply this out

  4. anonymous
    • one year ago
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    Okay

  5. misty1212
    • one year ago
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    let mt know what you get

  6. misty1212
    • one year ago
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    then we can finish quickly

  7. anonymous
    • one year ago
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    Alright, hold on:)

  8. anonymous
    • one year ago
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    -x^2+2x+8

  9. misty1212
    • one year ago
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    ok good

  10. anonymous
    • one year ago
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    :)

  11. misty1212
    • one year ago
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    now the fact that the leading coefficient it negative ( it is \(-1\)) means this parabola opens down all that is left is to find the vertex

  12. misty1212
    • one year ago
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    the first coordinate of the vertex of \(y=ax^2+bx+c\) is \[-\frac{b}{2a}\] which in your case is \[-\frac{2}{2\times (-1)}\]

  13. anonymous
    • one year ago
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    1

  14. misty1212
    • one year ago
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    right and the second coordinate is what you get for \(y\) when you replace \(x\) by \(1\)

  15. anonymous
    • one year ago
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    9

  16. misty1212
    • one year ago
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    right again

  17. misty1212
    • one year ago
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    so lets answer each question in order

  18. anonymous
    • one year ago
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    d=all real #'s right?

  19. misty1212
    • one year ago
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    Find the domian the domain of an polynomial is \(\mathbb{R}\) what you said

  20. misty1212
    • one year ago
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    the range since it is a parabola that opens down, and has a maximum at \(y=9\) the range is?

  21. anonymous
    • one year ago
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    y>=-9

  22. misty1212
    • one year ago
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    oh no

  23. anonymous
    • one year ago
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    Oh:( Ok

  24. misty1212
    • one year ago
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    not sure where you got the \(-9\) from it is \(9\) right?

  25. anonymous
    • one year ago
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    yes, whoops!

  26. misty1212
    • one year ago
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    and also the parabola opens down that means the MAXIMUM value is 9, not the minimum value

  27. misty1212
    • one year ago
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    |dw:1439235731008:dw|

  28. anonymous
    • one year ago
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    is maximum <=,>= or <,>

  29. misty1212
    • one year ago
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    lets forget about rules and think the possible values for \(y\) are numbers less than or equal to 9

  30. anonymous
    • one year ago
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    Alright

  31. misty1212
    • one year ago
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    if you want to write it as an inequality you can write \[y\leq 9\] or as an interval \[(-\infty, 9]\]

  32. anonymous
    • one year ago
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    okay, I see :)

  33. misty1212
    • one year ago
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    and finally, the axis of symmetry which we found ages ago is \(x=1\)

  34. misty1212
    • one year ago
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    done right?

  35. anonymous
    • one year ago
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    yes:)

  36. anonymous
    • one year ago
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    Thank you:)

  37. misty1212
    • one year ago
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    \[\color\magenta\heartsuit\]

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