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# just a bit of quick help please!! Watch

1. another question im stuck on........
the curve C with equation y=x^2 - 6x + 18 meets the y-axis at P and has a minimum point at Q.
sketch the graph of C, showing the coordinates of P and Q...
how would you work these 2 points out and what would the graph look like?
thanks if you could help
2. If you have a point x-coordinate must be zero, so to find P you need to substitute x=0 into the equation. This then gives P=(0,y), where y is to be found.

To find the minimum point you need to complete the square. Say you have . Then since any square number is always greater than or equal to zero, we have , and it is only equal to b when , which happens when , and so the minimum point must be at (-a,b). See if you can apply this to your problem.

When you plot the graph, you need to plot the minimum point (which is where the curve 'bends' back upwards), and the point where it crosses the y-axis. If you're feeling keen you can also find where it crosses the x-axis (i.e. the roots of the polynomial), and then you have more than enough information to make a convincing sketch.
3. (Original post by nuodai)
If you have a point x-coordinate must be zero, so to find P you need to substitute x=0 into the equation. This then gives P=(0,y), where y is to be found.

To find the minimum point you need to complete the square. Say you have . Then since any square number is always greater than or equal to zero, we have , and it is only equal to b when , which happens when , and so the minimum point must be at (-a,b). See if you can apply this to your problem.

When you plot the graph, you need to plot the minimum point (which is where the curve 'bends' back upwards), and the point where it crosses the y-axis. If you're feeling keen you can also find where it crosses the x-axis (i.e. the roots of the polynomial), and then you have more than enough information to make a convincing sketch.
thanks for the help i understand it all but i dont know what x^2 - 6x + 18 is in the form (x+a)^2+b
sorry but i cant really remember how to do it!
thanks if you could help further
4. (Original post by Jay1012)
thanks for the help i understand it all but i dont know what x^2 - 6x + 18 is in the form (x+a)^2+b
sorry but i cant really remember how to do it!
thanks if you could help further
isn't in the form , but you can put it in that form. Do you know how to complete the square?
5. (Original post by nuodai)
isn't in the form , but you can put it in that form. Do you know how to complete the square?
i just tried and got (x-3)^2 + 9 but i think that's wrong.
no i dont really know, can you help ? please
6. (Original post by Jay1012)
i just tried and got (x-3)^2 + 9 but i think that's wrong.
no i dont really know, can you help ? please
Why do you think it's wrong? It looks right to me.

So if then what is a? What is b? So what are the coordinates of the minimum point?
7. (Original post by nuodai)
Why do you think it's wrong? It looks right to me.

So if then what is a? What is b? So what are the coordinates of the minimum point?
so the minimum point is (-3, 9) ?

or you said it is (-a, b)
which would be (--3, 9)
= (3, 9)

so is it (-3, 9) or (3, 9) ?????
8. (Original post by Jay1012)
so the minimum point is (-3, 9) ?

or you said it is (-a, b)
which would be (--3, 9)
= (3, 9)

so is it (-3, 9) or (3, 9) ?????
I could just give you the answer but you'll probably learn something if I don't What do you think the answer is? Try investigating. If you're still stuck I'll give you a prod in the right direction.
9. (Original post by nuodai)
I could just give you the answer but you'll probably learn something if I don't What do you think the answer is? Try investigating. If you're still stuck I'll give you a prod in the right direction.
10. (Original post by Jay1012)
Well what writing the coordinate (p,q) means is that x=p and y=q.

What happens when you evaluate when ? What about when ?

What about if you just put or to find the resulting value of y? Which of the two resulting values of y is bigger?

So which do you think is the minimum value?
11. (Original post by nuodai)
Well what writing the coordinate (p,q) means is that x=p and y=q.

What happens when you evaluate when ? What about when ?

What about if you just put or to find the resulting value of y? Which of the two resulting values of y is bigger?

So which do you think is the minimum value?
i think it's (-3, 9) ??????????
12. (Original post by Jay1012)
i think it's (-3, 9) ??????????
Are you guessing or are you following my guidance? Show some of your working instead of giving final answers, then I can see if/where you're going wrong.
13. (Original post by nuodai)
Are you guessing or are you following my guidance?
no i read what you said and i think it's (-3, 9) ??
14. (Original post by Jay1012)
no i read what you said and i think it's (-3, 9) ??
Why do you think that? Show your working. I'll show you where you're going wrong.
15. (Original post by nuodai)
Why do you think that? Show your working. I'll show you where you're going wrong.
i really dont know........... doesn't matter thanks for the help anyway

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