BronxNerd Posted March 18, 2011 Report Share Posted March 18, 2011 I have been sitting here trying to solve this problem for like 45 minutes and I am going nuts! Here's the problem: Let f(x) =2x^2 - 12x + 5. Express f(x) in the form f(x) = 2(x-h)^2 - k. Thanks in advance! I would really appreciate the help! Reply Link to post Share on other sites More sharing options...
Drake Glau Posted March 18, 2011 Report Share Posted March 18, 2011 (edited) f(x) = 2x2 - 12x + 5Complete the Square2x2-12x=-52x2-12x+36=-5+362x2-12x+36=31From here I get lost...I don't know why. Pretty sure you pull the two out and factor but this isn't a perfect square factor so I don't know how to get it to the form you need...2(x2-6x+18)=31FactorAnd that's all I got O.oGoogled some and found that k=c-(b2/4a)and h=-(b/2a) also O.oThese two only work for when a=/=1Sooo k=5-[-122/(4*2)]=-13h=-[-12/(2*2)]=3So, f(x)=2(x-3)2-13?Maybe?^graphed using a calculator, y values are equal so that should be the correct equation Edited March 18, 2011 by Drake Glau 2 Reply Link to post Share on other sites More sharing options...
timtamboy63 Posted March 18, 2011 Report Share Posted March 18, 2011 f(x) = 2x2 - 12x + 52x2 - 12x = -52x2 - 12x + 18 = -5 + 182(x2 - 6x + 9) = 132(x - 3)2 = 13f(x) = 2(x - 3)2 - 13Enjoy 1 Reply Link to post Share on other sites More sharing options...
Drake Glau Posted March 18, 2011 Report Share Posted March 18, 2011 f(x) = 2x2 - 12x + 52x2 - 12x = -52x2 - 12x + 18 = -5 + 182(x2 - 6x + 9) = 132(x - 3)2 = 13f(x) = 2(x - 3)2 - 13Enjoy Where'd you get the 18? That would have been way easier for me. Thought completing the square was (0.5b)2? Reply Link to post Share on other sites More sharing options...
timtamboy63 Posted March 18, 2011 Report Share Posted March 18, 2011 It usually is, but in this case, you need to take out the 2, so its (0.25b)2Though, I didn't look at it that way, you can kinda tell what you need just by looking at it Reply Link to post Share on other sites More sharing options...
BronxNerd Posted March 18, 2011 Author Report Share Posted March 18, 2011 Thanks guys! You're life savers!! Reply Link to post Share on other sites More sharing options...
Drake Glau Posted March 18, 2011 Report Share Posted March 18, 2011 It usually is, but in this case, you need to take out the 2, so its (0.25b)2Though, I didn't look at it that way, you can kinda tell what you need just by looking at it That's still only 9 I'm so confused lol Reply Link to post Share on other sites More sharing options...
timtamboy63 Posted March 18, 2011 Report Share Posted March 18, 2011 (edited) Oh yeah, then you gotta multiply that by 2, because you end up taking two out. I dunno, I didn't do it that way, more just looked at it Oh, and no problem BronxNerd If you're wondering, heres what my thought process was:2x2 - 12x = -52(x2 - 6x) = -5Once I had that, I knew that I needed a square, so it's (0.5b)2, which gives you:2(x2 - 6x + 9) = -52x2 - 12x + 18 = -5Only now, i've added 18, so i need to do that to the other side:2x2 - 12x + 18 = -5 + 18etc.At least, I think thats what it was Edited March 18, 2011 by timtamboy63 Reply Link to post Share on other sites More sharing options...
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