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Maths Difficulty.....Please Help Somebody :)

"Complete The Square For the Following Quadratic, then state a value of x which gives the least/minimum value. quadratic: 3x^2 + 8x + 16"

i know how to complete the square, but i dont understand what the second part of the question is about...please help!!

Reply 1

cimmie

x=-4/3

f'(x):6x+8
=>6x+8=0
<=>x=-4/3

sorry its just guessed :biggrin:

Reply 2

++Hex++

8

clever_lad

"Complete The Square For the Following Quadratic, then state a value of x which gives the least/minimum value. quadratic: 3x^2 + 8x + 16"

i know how to complete the square, but i dont understand what the second part of the question is about...please help!!

The least value is the bottom of the parabola. In (x + a)2 , '-a' will be the value of x that you need as it will make the brackets zero. The lowest y coordinate will be the constant.

Reply 3

Bhaal85

9

clever_lad

"Complete The Square For the Following Quadratic, then state a value of x which gives the least/minimum value. quadratic: 3x^2 + 8x + 16"

i know how to complete the square, but i dont understand what the second part of the question is about...please help!!

f(x) = 3[(x-1r1r3)^2+10r2r3] in completed square form

Reply 4

clever_lad

OP

thankyou hex :smile:

Reply 5

Bhaal85

9

Bhaal85

f(x) = 3[(x-1r1r3)^2+10r2r3] in completed square form

Thats 3 outside the whole equation. Bracket, x minus one and one third, close bracket squared, plus 10 and two thirds.

Reply 6

cimmie

is my answer right?
at the bottom of the parabola is f'(x)=0... if f'(x)=0 then x=-4/3 :confused:

Reply 7

++Hex++

8

clever_lad

thankyou hex :smile:

No problem :wink:

Reply 8

Bhaal85

9

Bhaal85

Thats 3 outside the whole equation. Bracket, x minus one and one third, close bracket squared, plus 10 and two thirds.

Therefore the vertex would be at x=4/3, positive not equal and Y=??? try and work it out. :biggrin:

Reply 9

Bhaal85

9

cimmie

is my answer right?
at the bottom of the parabola is f'(x)=0... if f'(x)=0 then x=-4/3 :confused:

You differentiated it. Why?

Reply 10

theone

Bhaal85

You differentiated it. Why?

To find the minimum.

Reply 11

Bhaal85

9

clever_lad

"Complete The Square For the Following Quadratic, then state a value of x which gives the least/minimum value. quadratic: 3x^2 + 8x + 16"

i know how to complete the square, but i dont understand what the second part of the question is about...please help!!

This person just wanna know where the vertex, i.e co-ordinate of the lowest point. Not the gradient.

Which is at x=4/3 and Y=32

Reply 12

clever_lad

OP

hex, i completed the square of 3x^2 + 8x + 16

the answer in completed square form is: 3(x + 4)^2 + 32

i then want to find the minimum/least value, and the value of "x" at which this occurs.

Is The minimum value zero, which occurs when x = -4? is this correct or not mate?

Reply 13

Bhaal85

9

clever_lad

hex, i completed the square of 3x^2 + 8x + 16

the answer in completed square form is: 3(x + 4)^2 + 32

i then want to find the minimum//east value, and the value of "x" at which this occurs.

Is The minimum value zero, which occurs when x = -4? is this correct or not mate?

Thats not right. :eek:

Look at my working out.

Reply 14

clever_lad

OP

i am correct, you dont ahve a clue what you are talking about

Reply 15

Juwel

18

Please can someone go through the 'completing the square' general case procedure for me? It's been a while since Methods you see...

Reply 16

Bhaal85

9

clever_lad

i am correct, you dont ahve a clue what you are talking about

If you say so. I have an A level in maths. I am sure there are many people who will say the same thing, your arrogance has made you dull, dont expect anymore help from me.

Reply 17

Bhaal85

9

ZJuwelH

Please can someone go through the 'completing the square' general case procedure for me? It's been a while since Methods you see...

Which method? Is it the basic one where the coefficient of x^2 is just one, or where its greater than one?

Reply 18

theone

ZJuwelH

Please can someone go through the 'completing the square' general case procedure for me? It's been a while since Methods you see...

Sure, all quadratics can be written in the form x^2 +bx + c.

Now we can note by multiplying out that this is in fact equal to (x+(b/2))^2 + (c - b^2/4).

This procedure of getting the second equation from the first is called completing the square.

By extending this you can work out the more general formula for the solution of a quadratic.