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# Maths graphs watch

1. why does putting an equation into completed square form show the vertex of the graph?

So for example:
f(x) = x2 + 4x + 3
In completed square form is x = -2 +- root1 (I think)
And from this the vertex is (-2,-1)

But why?
2. (Original post by surina16)
why does putting an equation into completed square form show the vertex of the graph?

So for example:
f(x) = x2 + 4x + 3
In completed square form is x = -2 +- root1 (I think)
And from this the vertex is (-2,-1)

But why?
I am afraid you didn't complete the square properly.
the ans is ((x+2)^2) -1
3. As Azhar said, the square wasn't completed properly. But imagine you had the graph y = f(x) where f(x) = x2

Have you learnt graph translations?

What if we had y = f(x+2)? This means f(x+2) = (x+2)2 !

What does f(x+2) mean from the f(x) graph? It means that the graph is shifted 2 units to the left.

So what if we plonk on your -1?

y = f(x+2) - 1

this means we get y = (x+2)2 - 1, which happens to be your graph.

What does a translation of y = f(x+2) - 1 represent? It represents shifting to the left 2 units, as we saw earlier. But NOW we have this -1 outside. So what happens if we take away 1 from all f(x+2) values? The graph shifts down by 1 unit.

So in your example, the y = x2 graph shifted 2 units left and 1 unit down where the original vertex was the origin. What happens to the point (0, 0) when shifted 2 left and 1 down? It becomes (-2, -1)
4. (Original post by surina16)
why does putting an equation into completed square form show the vertex of the graph?

So for example:
f(x) = x2 + 4x + 3
In completed square form is x = -2 +- root1 (I think)
And from this the vertex is (-2,-1)

But why?
I'll complete the square correctly for you: .

Now, since you know that square quantities are always then the minimum value of this expression occurs when the squared term is zero.

This means that occurs precisely when .

The minimum value of function at the point is .
5. (Original post by Azhar Rana)
I am afraid you didn't complete the square properly.
the ans is ((x+2)^2) -1
How did you get that? this is what I did:

x^2 + 4x + 3 = 0
(x+2)^2 -4 + 3 = 0
(x+2)^2 - 1 = 0
(x+2)^2 = 1
x+2 = +-root 1
x= -2 +- root 1

which bit was wrong?
6. (Original post by surina16)
How did you get that? this is what I did:

x^2 + 4x + 3 = 0
(x+2)^2 -4 + 3 = 0
(x+2)^2 - 1 = 0
(x+2)^2 = 1
x+2 = +-root 1
x= -2 +- root 1

which bit was wrong?
That's not the vertex, that's you finding the roots of the quadratic. Oh, and .

Also: moved to maths.
7. (Original post by Student403)
...
Damn, you win this one. At least our explanations are substantially different to warrant the ninja.
8. (Original post by Azhar Rana)
I am afraid you didn't complete the square properly.the ans is ((x+2)^2) -1
(Original post by Student403)
As Azhar said, the square wasn't completed properly. But imagine you had the graph y = f(x) where f(x) = x2

Have you learnt graph translations?

What if we had y = f(x+2)? This means f(x+2) = (x+2)2 !

What does f(x+2) mean from the f(x) graph? It means that the graph is shifted 2 units to the left.

So what if we plonk on your -1?

y = f(x+2) - 1

this means we get y = (x+2)2 - 1, which happens to be your graph.

What does a translation of y = f(x+2) - 1 represent? It represents shifting to the left 2 units, as we saw earlier. But NOW we have this -1 outside. So what happens if we take away 1 from all f(x+2) values? The graph shifts down by 1 unit.

So in your example, the y = x2 graph shifted 2 units left and 1 unit down where the original vertex was the origin. What happens to the point (0, 0) when shifted 2 left and 1 down? It becomes (-2, -1)
(Original post by Zacken)
I'll complete the square correctly for you: .

Now, since you know that square quantities are always then the minimum value of this expression occurs when the squared term is zero.

This means that occurs precisely when .

The minimum value of function at the point is .
Ah, that makes sense! Thank you everyone
9. (Original post by Zacken)
Damn, you win this one. At least our explanations are substantially different to warrant the ninja.
7.5/11

And yeah! I think yours is a lot simpler though And ofc in maths simpler = better
10. (Original post by Student403)
7.5/11

And yeah! I think yours is a lot simpler though And ofc in maths simpler = better
Daaamn, getting there. K : D ratio

Nah, I think yours is just as nice (if not nicer), transformations can be a very elegant thing!
11. (Original post by Zacken)
Daaamn, getting there. K : D ratio

Nah, I think yours is just as nice (if not nicer), transformations can be a very elegant thing!
K/D omg lol

Thanks! I do love translations because they seem so intuitive to me
12. (Original post by Zacken)
That's not the vertex, that's you finding the roots of the quadratic. Oh, and .

Also: moved to maths.
13. (Original post by Zacken)
Damn, you win this one. At least our explanations are substantially different to warrant the ninja.
lol, you guys
14. (Original post by surina16)
Remember: has the vertex at but the roots at - they are two different things.

No problem.
15. (Original post by surina16)
How did you get that? this is what I did:

x^2 + 4x + 3 = 0
(x+2)^2 -4 + 3 = 0
(x+2)^2 - 1 = 0
(x+2)^2 = 1
x+2 = +-root 1
x= -2 +- root 1

which bit was wrong?
remember,
y=x^2 the vertex is (0,0)
applying transformation
x+2 shifts x to the -ve x axis by 2 units.
y=(x)^2 -1
here we shif the Y by 1 in the -ve y axis.
so, the result is (x-2)^2 -1 the vertex is now -2,1
the vertex is shifted in the -x axis by 2 units and 1 unit in the -y direction,

hence the vertex is (-2,-1)
16. (Original post by Azhar Rana)
lol, you guys

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