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LaynaMae Group Title

ANYONE ?? Graphing Quadratics HELPP ! (Question 1 and answer is attached) Graph one of your 2nd degree functions from question 1. Identify which function you used and the key features of your graph. Explain how to find them algebraically.

  • 11 months ago
  • 11 months ago

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  1. LaynaMae Group Title
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  2. triston_mccain Group Title
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    the answer is message me!!

    • 11 months ago
  3. LaynaMae Group Title
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    @amistre64 @Luigi0210 @Compassionate

    • 11 months ago
  4. LaynaMae Group Title
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    @AllTehMaffs @johnweldon1993 ?

    • 11 months ago
  5. johnweldon1993 Group Title
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    We'll work with the f(x) f(x) = (x - 2)(x + 2) Alright it's important to remember this is the FACTORED version of a function...what this shows is where the zeros (x-intercepts) of the function are... What value(s) of 'x' make (x - 2)(x + 2) = 0 ??

    • 11 months ago
  6. LaynaMae Group Title
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    Oh God .. I have NO idea .... I don't get any of this , I had help on question 1 as well :/

    • 11 months ago
  7. johnweldon1993 Group Title
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    Alright no problem we'll walk through it :)

    • 11 months ago
  8. LaynaMae Group Title
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    Oh my goodness thank you so much ..

    • 11 months ago
  9. johnweldon1993 Group Title
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    Okay....so we have f(x) = (x - 2)(x + 2) Like I said above...seeing a function in this factored form...lets us find out where the zeros (also known as the x-intercepts) of the graph are... This is done by setting this form = to 0...so (x - 2)(x + 2) = 0 Okay...we know that anything times 0 = 0 right?

    • 11 months ago
  10. johnweldon1993 Group Title
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    Since we know...we can see that there are 2 values of 'x' that would make this function = 0... (x - 2)(x + 2) = 0 Well...we know that if x = 2.... (2 - 2)(2 + 2) = 0 ( 0) (4) = 0 Well indeed as we know 0 times 4 DOES = 0...so x = 2 would be one x-intercept... To find the other...if x = -2 we have (-2 - 2)(-2 + 2) = 0 ( -4 ) (0) = 0 Again it is true that -4 times 0 = 0...so -2 is ANOTHER x-intercept for the graph...

    • 11 months ago
  11. johnweldon1993 Group Title
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    so far we just have the 2 x-intercepts...this looks like |dw:1386883312282:dw|

    • 11 months ago
  12. LaynaMae Group Title
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    So is that all it's asking me to do ? :o

    • 11 months ago
  13. johnweldon1993 Group Title
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    Not quite...almost done though :) are you with me through what I've done so far?

    • 11 months ago
  14. LaynaMae Group Title
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    Ehh , kind of ... It's just a lot of information

    • 11 months ago
  15. johnweldon1993 Group Title
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    I know, trying to explain it well :/ lol just try to remember in this factored form...set the equation = to 0....and solve for 'x' (x + 2)(x - 2) = 0 We knew either x+2 had to equal 0... or we know that x-2 had to equal 0... So that's how we solved for the 2 x-intercepts... maybe a little summary better?

    • 11 months ago
  16. LaynaMae Group Title
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    That was a lot easier to understand :)

    • 11 months ago
  17. johnweldon1993 Group Title
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    Awesome! :) Okay....so now...do you know how to expand this factored form?? to make it look something like x² + bx + c

    • 11 months ago
  18. LaynaMae Group Title
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    Omg no :'(

    • 11 months ago
  19. johnweldon1993 Group Title
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    Don't get down...this is a pretty simple process...stay with me :)

    • 11 months ago
  20. johnweldon1993 Group Title
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    We have... (x - 2)(x + 2) in order to expand this to a quadratic function...we use the FOIL method... it says... Take the first term in the first parenthesis...and multiply it by each term in the second parenthesis... Redo this with the second term in the first parenthesis... Sound understandable? I'm going to do it out anyways lol

    • 11 months ago
  21. johnweldon1993 Group Title
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    so..."Take the first term in the first parenthesis...and multiply it by each term in the second parenthesis..." The first term in the first parenthesis (x - 2) is 'x' right? So we multiply it by each term in the second parenthesis (x + 2) so x times x = ? x times 2 = ? Now we just redo this for the second term in the first parenthesis (x - 2) which would be -2 so -2 times x = ? -2 times 2 = ? Fill in those question marks for me :)

    • 11 months ago
  22. LaynaMae Group Title
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    Wait fill out the first 2 question marks or the second 2 ..?

    • 11 months ago
  23. johnweldon1993 Group Title
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    Both :)

    • 11 months ago
  24. LaynaMae Group Title
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    Ok well the first 2 are: x times x = 1 ? and x times 2 = 2x ? Second 2: -2 times x = -2x ? and -2 times 2 = -4 ?

    • 11 months ago
  25. johnweldon1993 Group Title
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    Oh so close...everything is right but what is x times x? x times x is x² right?

    • 11 months ago
  26. LaynaMae Group Title
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    Ohhh yeah ! That makes more sense !!

    • 11 months ago
  27. johnweldon1993 Group Title
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    Alright perfect! so altogether we have x² + 2x - 2x - 4 Anything look like it can be simplified?

    • 11 months ago
  28. LaynaMae Group Title
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    @johnweldon1993 don't leave meee we're so close to finishing thisss D:

    • 11 months ago
  29. johnweldon1993 Group Title
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    lol no I'm not leaving openstudy is starting to lag on my computer...

    • 11 months ago
  30. johnweldon1993 Group Title
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    So back to that question... x² + 2x - 2x - 4 anything that can be simplified here?

    • 11 months ago
  31. LaynaMae Group Title
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    2x - 2x ?

    • 11 months ago
  32. johnweldon1993 Group Title
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    Right! what is 2x - 2x ??

    • 11 months ago
  33. LaynaMae Group Title
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    0 of course :p

    • 11 months ago
  34. johnweldon1993 Group Title
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    lol making sure you're paying attention :P Okay...so finally we just have x² - 4 Well...this is all we needed...because when we have a constant number in a quadratic...this is the y-intercept... so -4 would be this y-intercept... 2 x-intercepts at x = -2 and x = 2...and 1 y-intercept at -4 so altogether we have a graph that looks like... |dw:1386884802676:dw|

    • 11 months ago
  35. LaynaMae Group Title
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    And that's it ?? :o

    • 11 months ago
  36. johnweldon1993 Group Title
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    Thats it :) much easier to put it in a graphing calculator! lol

    • 11 months ago
  37. johnweldon1993 Group Title
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    And it's good because everything we just did...will act as your explanation of what the key features of your graph are...the x and y intercepts :)

    • 11 months ago
  38. LaynaMae Group Title
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    OMG THANK YOU SOO MUCH !! :DD

    • 11 months ago
  39. johnweldon1993 Group Title
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    Anytime :) I hope it all made sense!

    • 11 months ago
  40. johnweldon1993 Group Title
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    And if you ever need help with anything feel free to tag me in a question or message me :)

    • 11 months ago
  41. LaynaMae Group Title
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    I definitely will ! :)

    • 11 months ago
  42. LaynaMae Group Title
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    I actually need help with a question following this one !! :o @johnweldon1993

    • 11 months ago
  43. LaynaMae Group Title
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    Using your graph from question 4, describe if the average rate of change is increasing or decreasing, from left to right. Justify your observations with calculations.

    • 11 months ago
  44. johnweldon1993 Group Title
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    Oh sorry, didn't give me the notification you replied here... Well lets see...from (-infinity to 0) the function is decreasing....and from (0 to +infinity) the function is increasing...

    • 11 months ago
  45. LaynaMae Group Title
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    Right :o

    • 11 months ago
  46. johnweldon1993 Group Title
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    For the justification part... \[\large \frac{f(x_2) - f(x_1)}{x_2 - x_1}\] so say that from x = -4 to x = -1 we have f(x) = x² - 4 remember? so plug in x = -4 and x = -1 to that to get f(x2) and f(x1) f(x2) = -1² - 4 = -3 f(x1) = -4² - 4 = 12 so \[\large \frac{-3 - 12}{-1 + 4}\] \[\large \frac{-15}{3}\] \[\large -5 \] since this is a negative number we have a decreasing interval... make sense?

    • 11 months ago
  47. LaynaMae Group Title
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    Makes sense !

    • 11 months ago
  48. johnweldon1993 Group Title
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    Perfect :)

    • 11 months ago
  49. LaynaMae Group Title
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    So that's it ?? :o lol i'm a little slow

    • 11 months ago
  50. johnweldon1993 Group Title
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    Yeah that's it...if you wanted to do another calculation for the positive side you could but....yeah lol...and you're not slow you got exactly what I was saying :)

    • 11 months ago
  51. LaynaMae Group Title
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    Thank you againnn :)

    • 11 months ago
  52. johnweldon1993 Group Title
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    Of course :)

    • 11 months ago
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