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anonymous
 one year ago
Can someone help me, please?
The function f(t) = t2 + 12t − 18 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work.
anonymous
 one year ago
Can someone help me, please? The function f(t) = t2 + 12t − 18 represents a parabola. Part A: Rewrite the function in vertex form by completing the square. Show your work.

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Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3So first lets set this equation to 0. \(t^2+12t18=0\) Now keep the variables on the LHS but move the constants to the RHS. \(t^2 + 12t=18\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Any questions before continuing? :o

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not too sure what the RHS and the LHS stand for I think I have an idea but I want to be sure.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3RHS = Right Hand Side (of the equation) LHS = Left Hand Side (of the equation ) :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ah, okay that's what I thought. Thank you, just making sure.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Alright, continuing.. We're going to be expanding the LHS by completing the square, and to be consistent, whatever we do to the LHS of the equation, we must do to the RHS of the equation as well. Now in expanding the LHS, we need to create a quadratic function such that it fits the form \(ax^2+bx+c\). Right now we only have \(ax^2+bx\) but we're missing the \(c\). Following?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Alright good good. To expand the LHS, we need to find a \(c\) value. To do that we follow the formula: \(c= \left(\dfrac{b}{2}\right)^2\) Now what's our value of b?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3That's right, so if we substituted 12 in place of b, what would our cvalue be?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3That's correct :) We can now complete our quadratic by adding \(\color{red}{36}\) to both sides of our equation. We have now fit the quadratic form, \(ax^2+bx+c\) \(t^2+12t+\color{red}{36} = 18 + \color{red}{36}\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Now we simplify the LHS of our equation. \[(t+6)^2=18+36\] now we just simplify the right side, move it back over, and we're done!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, and to simplify the RHS you would just need to add 18 and 36, since there are no variables, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so it would end up: \[(t+6)^2=54\] Right?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Yep, and to fit the vertex form, \(y=a(xh)^2 +k\) , we just have to move the 54 over by subtracting it from both sides :)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[y=a(xh)^2+k \\ ~~~~~~~~~~~~~\downarrow \\ y=(t+6)^254\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is that the finished product or are we not finished? Because if we aren't finished, I'm not sure what to do after that.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Yep, we are done. \(\boxed{y=(t+6)^254}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay, thank you so much! That helped a lot.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Your question is asking you to rewrite the function, \(y=t^2+12t18\) in vertex form, \(y=(t+6)^254\) by completing the square :)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3No problem! Glad you were able to follow through :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I understand it a little bit more, too. I didn't understand it at all before cx

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Great! That's the goal of using OpenStudy  to answer homework questions and learn more about howto solve problems similar to the ones you are stuck on :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well thank goodness I found OpenStudy cx
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