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absurd AQA c1 questions watch

1. the graph y=f(x) is translated by 1 unit in the positive x direction and 4 units in the positive y direction to a graph of y=g(x)

find an expression for g(x) in the form ax^2 + bx +c

any ideas how I would do this?
2. What about the rest of the question
3. (Original post by TenOfThem)
What about the rest of the question
we need it?
4. (Original post by madfish)
we need it?
What's the original equation of the graph prior to transformation? i.e. what's f(x) equal to?
5. (Original post by Nistar)
What's the original equation of the graph prior to transformation? i.e. what's f(x) equal to?
(1-2x)(1+2x) i.e 1-4x^2
6. (Original post by madfish)
we need it?
that's half a question, you need to know f(x) to do it...

otherwise let f(x)=dx^2+ex+f and then c=f+4 (as an example, it actually isn't for your question) or whatever the translation was etc
7. I'm assuming f(x) was x^2?

f(x) = x^2
g(x) = (x-1)^2 + 4

And then expand to get g(x) in the form wanted in the question.

If f(x) is not x^2 then steps should be similar to above.
8. (Original post by madfish)
(1-2x)(1+2x) i.e 1-4x^2
So 1-4x2 needs to be translated 1 unit to the positive x direction and 4 units in the positive y direction.

The x-direction unit of 1 will change to a negative within the equation to represent that translation and needs to be added onto x itself. i.e. a translation of y=x by a units in the positive x-direction will be y=(x-a)

Then the translation by 4 units in the positive y-direction will just be added onto the end of the equation i.e. a translation of y=x by a units in the positive y-direction would be y=(x) + a

Work it out from there
9. (Original post by SherlockHolmes)
I'm assuming f(x) was x^2?

f(x) = x^2
g(x) = (x-1)^2 + 4

And then expand to get g(x) in the form wanted in the question.

If f(x) is not x^2 then steps should be similar to above.
sorry f(x)=(1-2x)(1+2x) i.e 1-4x^2
10. (Original post by Nistar)
So 1-4x2 needs to be translated 1 unit to the positive x direction and 4 units in the positive y direction.

The x-direction unit of 1 will change to a negative within the equation to represent that translation and needs to be added onto x itself. i.e. a translation of y=x by a units in the positive x-direction will be y=(x-a)

Then the translation by 4 units in the positive y-direction will just be added onto the end of the equation i.e. a translation of y=x by a units in the positive y-direction would be y=(x) + a

Work it out from there
Its the fact it's in the form 1-4x^2 is giving me trouble.. how would I change that equation to correspond with the translations?
11. This may help:

b - a = -a + b

1-4x^2 = -4x^2 + 1
12. (Original post by SherlockHolmes)
This may help:

b - a = -a + b

1-4x^2 = -4x^2 + 1
sorry to sound thick but I still don't get it ;(
13. (Original post by madfish)
Its the fact it's in the form 1-4x^2 is giving me trouble.. how would I change that equation to correspond with the translations?
Well if you've got 1-4x2, and following what I said in my earlier reply:
g(x)= 5-4(x-1)2

As subtracting 1 for the translation by 1 unit in the positive x-direction gives 1 - 4(x-1)2 , and translation by 4 units in the positive y-direction then gives 5 - 4(x-1)2

1-4x2 is also equal to -4x2 + 1 if that helps to make it clearer.
14. f(x) is translated by 1 unit in the positive x direction and 4 units in the positive y direction.

If f(x) is translated by 1 unit in the positive x direction, then f(x) becomes f(x-1)

If f(x) is translated 4 units in the positive y direction, then f(x) becomes f(x) + 4

Combining the two, f(x) becomes f(x-1) + 4
15. replace x with x - 1 in f(x)... then add 4

job done
16. (Original post by the bear)
replace x with x - 1 in f(x)... then add 4

job done
haha laughed at this a little , cheers bro
17. (Original post by madfish)
haha laughed at this a little , cheers bro
It's better to try and understand it too... TSR won't be with you in the exam to give you answers.
18. Giving you the answer isn't going to help you.

Say you have some function and at it has the value

If the graph has been translated by one unit in the positive x-direction, then at which value of do we have that ? Given that the graph has been essentially moved to the right by one, we see it no longer happens at but instead happens at , and all values gets shifted by one. How can this be expressed in terms of ? For simplicity, let's denote the translation by one unit in the positive x-direction by the function , so using the example we've already done

,

We can put this more generally

,

So, you should be able to tell, we can express in terms of . Specifically

Now, translation in the y-direction is easy. Let's go back to the original example of if we have and at it has the value

Translating the graph up by four units, it's easy to notice that the value at is not going to be but

If we're translating the graph up by 4 units, then, denoting this translation as a new function we get that

Because all y-values are going to increase by 4.

If we're combining these two translations we can express this as

The significance of showing is that it doesn't matter which transformation you do first, it doesn't make a difference.
19. (Original post by Noble.)

Say you have some function and at it has the value

If the graph has been translated by one unit in the positive x-direction, then at which value of do we have that ? Given that the graph has been essentially moved to the right by one, we see it no longer happens at but instead happens at , and all values gets shifted by one. How can this be expressed in terms of ? For simplicity, let's denote the translation by one unit in the positive x-direction by the function , so using the example we've already done

,

We can put this more generally

,

So, you should be able to tell, we can express in terms of . Specifically

Now, translation in the y-direction is easy. Let's go back to the original example of if we have and at it has the value

Translating the graph up by four units, it's easy to notice that the value at is not going to be but

If we're translating the graph up by 4 units, then, denoting this translation as a new function we get that

Because all y-values are going to increase by 4.

If we're combining these two translations we can express this as

The significance of showing is that it doesn't matter which transformation you do first, it doesn't make a difference.
thanks for that

but... If I do 1- 4(x-1)^2 + 4 this expands to -4x^2 - 2x + 4

which is the wrong answer... what am I doing wrong?
20. (Original post by madfish)
thanks for that

but... If I do 1- 4(x-1)^2 + 4 this expands to -4x^2 - 2x + 4

which is the wrong answer... what am I doing wrong?
Expanding incorrectly

5 - 4(x-1)^2 is NOT -4x^2 - 2x + 4

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