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Completing the square; for turning points. watch

1. Hi guys;

I have been studying "completing the square" in relation to Algebraic functions and graphs. I have learned that using "completing the square" will give you the turning point.

With x2 + 4x + 1 = 0

When I completed the square; I got the result of (x+2)2=3

Now, apparently; It gives us the vertex (turning point) of x2 + 4x + 1: (-2, -3).

However I am somewhat at a loss at how exactly those figures were derived.

2. (Original post by apronedsamurai)
Hi guys;

I have been studying "completing the square" in relation to Algebraic functions and graphs. I have learned that using "completing the square" will give you the turning point.

With x2 + 4x + 1 = 0

When I completed the square; I got the result of (x+2)2=3

Now, apparently; It gives us the vertex (turning point) of x2 + 4x + 1: (-2, -3).

However I am somewhat at a loss at how exactly those figures were derived.

Let's say a quadratic is generally . is just a transformation. It's shifted to the right by a units.
So the stationary point (0,b) becomes . The is just the equivalent y point as making the bracket 0 means that y=-b[/tex]
3. (Original post by keromedic)
I think you mean (-2,3)
No, -3 was the value given on the tutorial website.
4. (Original post by apronedsamurai)

With x2 + 4x + 1 = 0

When I completed the square; I got the result of (x+2)2=3

Now, apparently; It gives us the vertex (turning point) of x2 + 4x + 1: (-2, -3).

do not rearrange

you should realise that is 0 or positive

Therefore the whole thing is smallest when (x+2) = 0

So

(-2,-3)
5. So sorry; still not quite getting it.

I understand (x+2)=0; therefore; x=2. But what of -3? Is this what we call substitution; and this is the method used always?
6. (Original post by apronedsamurai)
So sorry; still not quite getting it.

I understand (x+2)=0; therefore; x=2. But what of -3? Is this what we call substitution; and this is the method used always?

What does that equal when the bracket is zero
7. Why have you made it =3? Move that 3 back to the other side before you get confused. The original equation was equal to 0....
8. (Original post by apronedsamurai)
...
It's fairly straightforward.

We know that for because if that bracket becomes negative, squaring it will make it positive and squaring that bracket if it was positive would make it positive: this means that the minimum must occur when therefore the vertex is . (The -3 comes from when you let .

(i hope i appeased you m8)

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