Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.

f(x) = (x − 8)^2
f(x) = (x − 4)^2 − 13
f(x) = (x − 4)^2 + 3
f(x) = (x − 4)^2 + 16

Question

Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. 

 f(x) = (x − 8)^2
 f(x) = (x − 4)^2 − 13
 f(x) = (x − 4)^2 + 3
 f(x) = (x − 4)^2 + 16

mrnood · Answer

well - you could expand all the answers and see which is the same as the original equation - but that is the long way round.

Look at the brackets which are all 'squared'

look at teh constant term  (e.g. -8 in the first example) when you square brackets you will always get the square of that value as a constant

so again in the first example you will get +64 as the constant when you expand
now - you can see that that is NOT the same as the original (the constant is +3 in the original)

So - go throught the answers and work out the resultant of the CONSTANT terms only. Only one of them works out to be +3 so that must be the answer

anonymous · Answer

Then wouln't it be the second one?

mrnood · Answer

:-)

mrnood · Answer

However - that is a quick 'cheat' given that itis a multichoice question.

To really complete your understanding you should use the 'compete the square' method as required by the question - if you didn't have the multichoice you would have to do that...