I need to write -x^2 + 6x -8 in the form f(x) = a(x-h)^2 + k Is it f(x) = -1(x+3)^2 -17
H haliebre New member Joined Apr 4, 2006 Messages 43 Apr 9, 2006 #1 I need to write -x^2 + 6x -8 in the form f(x) = a(x-h)^2 + k Is it f(x) = -1(x+3)^2 -17
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Apr 9, 2006 #2 Re: equations Hello, haliebre! I need to write −x2 + 6x − 8\displaystyle -x^2\,+\,6x\,-\,8−x2+6x−8 in the form f(x) = a(x − h)2 + k\displaystyle f(x)\:=\:a(x\,-\,h)^2\,+\,kf(x)=a(x−h)2+k Click to expand... Factor out -1: f(x) = −(x2 − 6x + 8)\displaystyle \:f(x)\;=\;-(x^2\,-\,6x\,+\,8)f(x)=−(x2−6x+8) Complete the square: f(x) = −(x2 − 6x\displaystyle \:f(x)\;=\;-(x^2\,-\,6xf(x)=−(x2−6x + 9 + 8\displaystyle +\,8+8 - 9) = −(x2 − 6x + 9 − 1)\displaystyle ) \;= \;-(x^2\,-\,6x\,+\,9\,-\,1))=−(x2−6x+9−1) f(x) = −[(x − 3)2 − 1] = −(x − 3)2 + 1\displaystyle \;\;f(x)\;=\;-[(x\,-\,3)^2\,-\,1] \;= \;-(x\,-\,3)^2\,+\,1f(x)=−[(x−3)2−1]=−(x−3)2+1
Re: equations Hello, haliebre! I need to write −x2 + 6x − 8\displaystyle -x^2\,+\,6x\,-\,8−x2+6x−8 in the form f(x) = a(x − h)2 + k\displaystyle f(x)\:=\:a(x\,-\,h)^2\,+\,kf(x)=a(x−h)2+k Click to expand... Factor out -1: f(x) = −(x2 − 6x + 8)\displaystyle \:f(x)\;=\;-(x^2\,-\,6x\,+\,8)f(x)=−(x2−6x+8) Complete the square: f(x) = −(x2 − 6x\displaystyle \:f(x)\;=\;-(x^2\,-\,6xf(x)=−(x2−6x + 9 + 8\displaystyle +\,8+8 - 9) = −(x2 − 6x + 9 − 1)\displaystyle ) \;= \;-(x^2\,-\,6x\,+\,9\,-\,1))=−(x2−6x+9−1) f(x) = −[(x − 3)2 − 1] = −(x − 3)2 + 1\displaystyle \;\;f(x)\;=\;-[(x\,-\,3)^2\,-\,1] \;= \;-(x\,-\,3)^2\,+\,1f(x)=−[(x−3)2−1]=−(x−3)2+1
G Gene Senior Member Joined Oct 8, 2003 Messages 1,904 Apr 9, 2006 #3 Hint: You can usually spot a wrong answer by pluging in a few values for x. f(0) = -0^2 + 6*0 -8 = -8 f(0) = -1(0+3)^2 -17 = -26 Not the same so not correct. ---------------- Gene
Hint: You can usually spot a wrong answer by pluging in a few values for x. f(0) = -0^2 + 6*0 -8 = -8 f(0) = -1(0+3)^2 -17 = -26 Not the same so not correct. ---------------- Gene
