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Completing the square/vertexs

Please could somebody help me with completing the square and finding vertexs - as in the question provided.

I have been taught to square the number in the brackets - in this case (3/2) and subtract that off, as I have done. However, in this question it seems the answer, which is (45/4) has added (9/4) - the square of (3/2) on. This is the complete opposite of what I thought should happen?

Any help would be appreciated.
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Original post by OL350
Please could somebody help me with completing the square and finding vertexs - as in the question provided.

I have been taught to square the number in the brackets - in this case (3/2) and subtract that off, as I have done. However, in this question it seems the answer, which is (45/4) has added (9/4) - the square of (3/2) on. This is the complete opposite of what I thought should happen?

Any help would be appreciated.


Your minus is misplaced, so when you expand (-x + 3/2)^2 out you'll get something fairly different from the original equation.

Can you see where it should go instead? This will help you with why the b/2 term should be added on.
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OL350
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Original post by SeanFM
Your minus is misplaced, so when you expand (-x + 3/2)^2 out you'll get something fairly different from the original equation.

Can you see where it should go instead? This will help you with why the b/2 term should be added on.


Thanks for the help. Taking into account what you've said the minus should go before all the brackets? This will then leave a minus minus a minus, giving a positive and thus why the fraction is added on as opposed to usually being subtracted.

Am am I right in saying the minus sign should always go in front on a -X^2 style question like this?
Original post by OL350
Thanks for the help. Taking into account what you've said the minus should go before all the brackets? This will then leave a minus minus a minus, giving a positive and thus why the fraction is added on as opposed to usually being subtracted.

Am am I right in saying the minus sign should always go in front on a -X^2 style question like this?


I think you've got it :smile: It's just like that for ax^2 as well. You've probably seen putting 2 or 3 in front of the brackets.
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Original post by SeanFM
I think you've got it :smile: It's just like that for ax^2 as well. You've probably seen putting 2 or 3 in front of the brackets.


Thanks.

A little unrelated but seen as this is a maths thread here goes...
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Have a differentiated the following correctly.

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Original post by OL350
Have a differentiated the following correctly.



You've differentiated it correctly but you didn't have the right term - it was fine until you were dealing with (x^5/2)^3 - you've multiplied both the numerator and the denominator by 3 to give you 15/6, which is the same as 5/2 so it's like you've never raised it to ^3. Can you spot what you should have done?

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