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Unformatted text preview: t into the form f ( x) = a ( x  h) + k
2 This will use a modified completing the square process. It’s probably best to do this with an
example. Example 3 Convert each of the following into the form f ( x ) = a ( x  h ) + k .
2 (a) f ( x ) = 2 x 2  12 x + 3 [Solution]
(b) f ( x ) =  x 2 + 10 x  1 [Solution]
Solution
Okay, as we pointed out above we are going to complete the square here. However, it is a
slightly different process than the other times that we’ve seen it to this point.
(a) The thing that we’ve got to remember here is that we must have a coefficient of 1 for the x2
term in order to complete the square. So, to get that we will first factor the coefficient of the x2
term out off the whole right side as follows. 3ö
æ
f ( x ) = 2 ç x2  6x + ÷
2ø
è
Note that this will often put fractions into the problem that is just something that we’ll need to be
able to deal with. Also note that if we’re lucky enough to have a coefficient of 1 on the x2 term
we won’t have...
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 Spring '12
 MrVinh

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