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anonymous

  • one year ago

***FAN AND MEDAL*** The second part of the new coaster is a parabola. 4)Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros. 5)The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.

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  1. anonymous
    • one year ago
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    @phi

  2. anonymous
    • one year ago
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    oh thats simple, what do u think

  3. anonymous
    • one year ago
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    i dont thats why im asking, im not good at math

  4. anonymous
    • one year ago
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    what grade r u in

  5. anonymous
    • one year ago
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    now im 10, but im take flvs algebra 1

  6. anonymous
    • one year ago
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    ok

  7. anonymous
    • one year ago
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    so read the question carefully again

  8. anonymous
    • one year ago
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    i will help

  9. anonymous
    • one year ago
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    thank you!!! finally!!

  10. anonymous
    • one year ago
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    but why u ignoreing me

  11. anonymous
    • one year ago
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    i tried to fan

  12. anonymous
    • one year ago
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    when someone help me and give the answers, i will be fan

  13. anonymous
    • one year ago
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    @jim_thompson5910

  14. anonymous
    • one year ago
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    @SolomonZelman @jdoe0001

  15. SolomonZelman
    • one year ago
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    have you chosen the parabola for question #4?

  16. SolomonZelman
    • one year ago
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    Make up any parabola that you like, that will be convinient for you to use. For example, i would make up the following parabola: y=-x²+4x+5

  17. SolomonZelman
    • one year ago
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    want to use this example, or do you want to use your own example (if you want to use your own example, then make one up)

  18. anonymous
    • one year ago
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    i want to use your example ;/ @SolomonZelman

  19. anonymous
    • one year ago
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    are you there @SolomonZelman

  20. SolomonZelman
    • one year ago
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    ok, we need to find the vertex. y=-x²+4x+5 y=-(x²-4x)+5 what number would you want y=-(x²-4x+\(\color{red}{\rm here}\))+5 to make the expression in parenthesis a perfect square?

  21. anonymous
    • one year ago
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    i can use number 5?

  22. SolomonZelman
    • one year ago
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    you need to make the part inside the parenthesis into a perfect square trinomial.... do you know what a perfect square trinomial is?

  23. anonymous
    • one year ago
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    no ;/

  24. SolomonZelman
    • one year ago
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    you know that (x+a)² would be expanded the following way: (x+a)² = (x+a)(x+a) = x²+ax+ax+a² = x²+2ax+a² (do you know this?)

  25. anonymous
    • one year ago
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    you ask me if i know how to do this?

  26. SolomonZelman
    • one year ago
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    yes, if you followed the steps i did , and if you would be able to expand similar expressions like this on your own.

  27. anonymous
    • one year ago
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    i see its not really hard to understand that

  28. SolomonZelman
    • one year ago
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    ok, very good!

  29. SolomonZelman
    • one year ago
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    So, what we have as the result, the x²+2ax+a² is called a perfect square trinomial

  30. SolomonZelman
    • one year ago
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    this is an expression that can be factored into (x+a)²

  31. SolomonZelman
    • one year ago
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    (of course, a is some constant, and x is the variable)

  32. SolomonZelman
    • one year ago
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    Ok, can you expand (x+1)² for me?

  33. anonymous
    • one year ago
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    ok wait

  34. SolomonZelman
    • one year ago
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    sure, take your time.

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

  36. anonymous
    • one year ago
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    its that right?

  37. SolomonZelman
    • one year ago
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    i am trying to undertsnad line 1 and 3....

  38. SolomonZelman
    • one year ago
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    there is a rule for this: \(\large\color{black}{ \displaystyle (b+a)^2= b^2+2ba+a^2 }\) and so it would be true in this case: \(\large\color{black}{ \displaystyle (x+a)^2= x^2+2xa+a^2 }\) and same way, we can say: \(\large\color{black}{ \displaystyle (x+1)^2= x^2+2x(1)+(1)^2=x^2+2x+1 }\)

  39. SolomonZelman
    • one year ago
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    (we are just expanding....)

  40. SolomonZelman
    • one year ago
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    but an expression that is in the form of x²+2ax+a² is the "perfect square trinomial" it is prefect square because it takes to multiply (x+a) times (x+a) to get it...

  41. SolomonZelman
    • one year ago
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    following so far?

  42. anonymous
    • one year ago
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    mmum yea..

  43. SolomonZelman
    • one year ago
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    So, now lets think it backwards.

  44. anonymous
    • one year ago
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    ok... so?

  45. SolomonZelman
    • one year ago
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    This (below) is an example of how to find the last term for a perfect square trinomial... Say I have \(\large\color{black}{ \displaystyle x^2+6x }\) and I want to know what number to add \(\large\color{black}{ \displaystyle x^2+6x+\color{red}{\rm here} }\) to make this expression a "perfect square trinomial" \(\rm \large Lets~~compare!\) \(\large\color{black}{ \displaystyle x^2+6x+\color{red}{\rm here} }\) (our expression where we want to add a number to make it a perfect square trinomial) \(\large\color{black}{ \displaystyle x^2+2ax+a^2 }\) (the general form of a perfect square trinomial) So you can see based on the first 2 terms of each of the expressions that the "2a" part in our case is 6. So if 2a is 6, then a is 3, and then a² is 9. So we would want to add 9 to make our expression a perfect square trinomial. \(\large\color{black}{ \displaystyle x^2+6x+\color{red}{\rm 9} }\)

  46. SolomonZelman
    • one year ago
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    And so it would always follow, that when you have: \(\large\color{black}{ \displaystyle x^2+\color{red}{\rm c}x }\) then the number you have to add to make the expression into a perfect square trinomial is: \(\large\color{black}{ \displaystyle \frac{\color{red}{\rm c} ^2}{4}}\)

  47. SolomonZelman
    • one year ago
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    if you have a question ask.... or if you are getting it, say so... (if you need more time to read, then keep reading)

  48. anonymous
    • one year ago
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    @jim_thompson5910

  49. SolomonZelman
    • one year ago
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    do i know the answer... i don't really know the question.... what is the first part of the roller coaster, if you are asked to create the second one?

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