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Janu16
 one year ago
Using the completingthesquare method, rewrite f(x) = x2 − 8x + 3 in vertex form.
Janu16
 one year ago
Using the completingthesquare method, rewrite f(x) = x2 − 8x + 3 in vertex form.

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2Ok, tell me this: Say, you have: \(x^28x\) THEN, what number would you want to add to the end, to make that a perfect square trinomial?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle x^2\pm\color{red}{\rm 2a}x+\color{red}{\rm a}^2 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2Does this look familiar to anything?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2`(x  a)² = x²  2a + a²` `(x + a)² = x² + 2a + a²`

Janu16
 one year ago
Best ResponseYou've already chosen the best response.0umm no. I learned this but can't get the answer

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2you know those two in gray, right?

Janu16
 one year ago
Best ResponseYou've already chosen the best response.0sum and difference of a cube??

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2No cubes: Just how to expand (x+a)^2 and (xa)^2

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2So, we are going to make x^28x (by adding some number) into x^22a+a^2 form

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2\(\large\color{black}{ \displaystyle x^2\color{red}{\rm 2a}x+\color{red}{\rm a}^2 =(x\color{red}{\rm a})^2 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2So if 2a is 8, than a is 4. Right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.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^28x, to make our polynomial a perfect square.

Janu16
 one year ago
Best ResponseYou've already chosen the best response.0what is this formula called? cause I didn't learn this?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2oh, don't worry, you can just google (a+b)^2 and all of that will come up

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2all of those like (a+b)^2 and (ab)^2 ... it will all show up.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2We 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: \(\large\color{black}{ \displaystyle x^2\color{red}{\rm 8}x\color{blue}{}+3 }\) \(\large\color{black}{ \displaystyle x^2\color{red}{\rm 8}x\color{blue}{+1616}+3 }\) \(\large\color{black}{ \displaystyle (x^2\color{red}{\rm 8}x+16)16+3 }\) in parenthesis, it is a perfect square trinomial and 16+3 is 13.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2you mixed up something a little, how did you get that result/

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.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 \(x628x\) 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: \(\large\color{black}{ \displaystyle x^2\color{red}{\rm 8}x\color{blue}{}+3 }\) \(\large\color{black}{ \displaystyle x^2\color{red}{\rm 8}x\color{blue}{+1616}+3 }\) \(\large\color{black}{ \displaystyle (x^2\color{red}{\rm 8}x+16)16+3 }\) I added a magic zero, so to speak. +1616, 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 `a²2a+a²=(xa)²`, and thus we get the following: \(\large\color{black}{ \displaystyle (x\color{red}{ 4})^213 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2read it carefully, and if you have questions, then ask.

Janu16
 one year ago
Best ResponseYou've already chosen the best response.0ohok tysm!! so you just simplied 8 to 4?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2oh, the result I showed at the end can't be simplified. You can rewrite it to what it was in the beginning if you do the inverse operations.

Janu16
 one year ago
Best ResponseYou've already chosen the best response.0ohhhok f(x) = (x − 4)2 − 13 this would be the answer right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.2(x4)\(\color{red}{^2}\)13 :D

Janu16
 one year ago
Best ResponseYou've already chosen the best response.0tysm! can you hep with other one on new thread plz?
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