A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Janu16

  • one year ago

Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

  • This Question is Closed
  1. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Ok, tell me this: Say, you have: \(x^2-8x\) THEN, what number would you want to add to the end, to make that a perfect square trinomial?

  2. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    8? I think

  3. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    probably not

  4. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \(\large\color{black}{ \displaystyle x^2\pm\color{red}{\rm 2a}x+\color{red}{\rm a}^2 }\)

  5. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Does this look familiar to anything?

  6. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    `(x - a)² = x² - 2a + a²` `(x + a)² = x² + 2a + a²`

  7. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    umm no. I learned this but can't get the answer

  8. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait i know that

  9. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you know those two in gray, right?

  10. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sum and difference of a cube??

  11. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    No cubes: Just how to expand (x+a)^2 and (x-a)^2

  12. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohok

  13. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    So, we are going to make x^2-8x (by adding some number) into x^2-2a+a^2 form

  14. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok

  15. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 2a}x+\color{red}{\rm a}^2 =(x-\color{red}{\rm a})^2 }\)

  16. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    So if 2a is 8, than a is 4. Right?

  17. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ya

  18. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    than you square it?

  19. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 8}x+\color{red}{\rm 4}^2 =(x-\color{red}{\rm 8})^2 }\) \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 8}x+16 =(x-\color{red}{\rm 8})^2 }\) that would be a perfect square trinomial. So we add 16 to the x^2-8x, to make our polynomial a perfect square.

  20. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    what is this formula called? cause I didn't learn this?

  21. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    which formula?

  22. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the one you are using

  23. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    oh, don't worry, you can just google (a+b)^2 and all of that will come up

  24. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    all of those like (a+b)^2 and (a-b)^2 ... it will all show up.

  25. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okk

  26. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    We will add 16, but we can NOT just add 16, because we will change the value of the trinomial. So this is what we will do: \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 8}x\color{blue}{}+3 }\) \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 8}x\color{blue}{+16-16}+3 }\) \(\large\color{black}{ \displaystyle (x^2-\color{red}{\rm 8}x+16)-16+3 }\) in parenthesis, it is a perfect square trinomial and -16+3 is -13.

  27. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so it would be -8-13+3

  28. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    you mixed up something a little, how did you get that result/

  29. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    ??

  30. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    from that equation

  31. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait x- 8 - 13?

  32. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 2a}x+\color{red}{\rm a}^2 =(x-\color{red}{\rm a})^2 }\) And we want to get our \(x62-8x\) into that form, by adding a value. We will add 16, but we can NOT just add 16, because we will change the value of the trinomial. So this is what we will do: \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 8}x\color{blue}{}+3 }\) \(\large\color{black}{ \displaystyle x^2-\color{red}{\rm 8}x\color{blue}{+16-16}+3 }\) \(\large\color{black}{ \displaystyle (x^2-\color{red}{\rm 8}x+16)-16+3 }\) I added a magic zero, so to speak. +16-16, is all I did:) in parenthesis, it is a perfect square trinomial and -16+3 is -13. \(\large\color{black}{ \displaystyle (x^2{~}-{~} 2\times\color{red}{ 4}x{~}+{~}\color{red}{ 4}^2)-13 }\) do you see that x\(^2\)-2a+a\(^2\) form in the parenthesis? We know that `a²-2a+a²=(x-a)²`, and thus we get the following: \(\large\color{black}{ \displaystyle (x-\color{red}{ 4})^2-13 }\)

  33. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    read it carefully, and if you have questions, then ask.

  34. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohok tysm!! so you just simplied 8 to 4?

  35. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    oh, the result I showed at the end can't be simplified. You can re-write it to what it was in the beginning if you do the inverse operations.

  36. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ohhhok f(x) = (x − 4)2 − 13 this would be the answer right?

  37. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    (x-4)\(\color{red}{^2}\)-13 :D

  38. Janu16
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    tysm! can you hep with other one on new thread plz?

  39. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.