Completing the square problem

[Chi]

The answer is (x+13/4)^2+87/16

I don’t understand why my y coordinate is different 87/8 not 87/16 is it because i multiplied everything by 2 or because I can’t spot my mistake

 

[Dr.Peterson]

Yes, it's because you multiplied the expression by 2 at the start, so you (correctly) found the minimum of twice the teacher's LHS.

But that is not an error! There is nothing wrong in clearing fractions by multiplying both sides of an inequality by 2. You have shown that the minimum of your LHS is 87/8, which is correct (though you did omit a 2, as marked). Nothing in the problem says that you have to find the minimum of the undoubled LHS; you have successfully shown that the given inequality is true.

Possibly your teacher, expecting to see the minimum of the expression he used, and also seeing the omitted 2 that made your final expression look like his, accidentally confused the two. Or perhaps you are being considered wrong merely for not doing exactly what the teacher did. (I hope not.)

 

[Chi]

Thank you very much.So just to clarify what I did was right then?

 

[Dr.Peterson]

I think so, as far as the main course of your work went.

What you failed to do, which would have helped, is to state explicitly what expression you were finding the minimum of. And of course you did omit a 2, so it is appropriate to take something off your score.

 

[Deleted member 4993]

The answer is (x+13/4)^2+87/16

I don’t understand why my y coordinate is different 87/8 not 87/16 is it because i multiplied everything by 2 or because I can’t spot my mistake

Was your problem originally:


Then:

we need to prove:

x² + 6x +18 - 2 -x/2 > 0

2x² + 13x + 32 > 0

Picture of your work got clipped-off on the left hand side.

 

[Chi]

Was your problem originally:
Yes it was
View attachment 12358

Then:

we need to prove:

x² + 6x +18 - 2 -x/2 > 0

2x² + 13x + 32 > 0

Picture of your work got clipped-off on the left hand side.

 

[Chi]

This is the markscheeme