Help with functions.

[SZ11]

I'm really weak with functions and I usually can't understand the questions. Functions is the part of the syllabus the I have the most problems with.
One of those problems is the 'completing square' method.
If someone could explain to me how it's done I would be very grateful.

Q) Express 4x^2 + 2x +3 in the form a(x+b)^2 + c. Where a , b and c are constants.

I have no idea how to do this. Help.

 

[Mohammad Aamer]

Try to this by steps..
1. Make the coefficient of x square 1 as follows..
4(x^2+ .5x )+3
2.Divide the second number in the bracket by 2 and square the bracket as follows..
4(X+.25)^2+ 3 - 4(.25)^2
{the - 4(.25)^2 comes because we need to retain the orignal function and if we do not add this we'll some other function when we open the brackets }
thus, 4(X+.25)^2+ 2.75 [a=4; b=.25; c=2.75]
We are just expressing the function in another form so if we open the brackets we should get the original form..
4(x^2+.5x+.0625)+2.75
thus 4x^2+2x+.25+2.75
thus 4x^2+2x+ 3
this can be used for checking your working...
and one more thing ...ive done everything in decimals cuz of inconvenience...we should use fractions.

 

[limca22334]

m

 

[Mohammad Aamer]

thank you aamer .....
additionally can someone help me? i have a function problem too but my problem is understanding: eg/ when i do a question (functions) and it asks me to complete the square. after that it says state the range of the function?? :S........also the second part asks me to state with a reason if that function has an inverse (based on the complete square method)?

And also if someone could just underline the main concept of one to one and one to many functions and how would we know if that has an inverse. THANKYOU
THIS QUESTION WAS IN OCT/NOV 06 last Question
Guys please help me out!

Whenever they're asking you to state y f doesnt have an inverse...you've to state that the function is not one-one. one-one function means that one value of fx/y has more than one value of x ....not based on completing the square. x^2 usually means that f isnt one-one. Hope u understood a bit .