just a bit of quick help please!!

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 $y=(x+a)^2+b$. Then since any square number is always greater than or equal to zero, we have $y \ge b$, and it is only equal to b when $(x+a)^2=0$, which happens when $x=-a$, 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

$x^2-6x+18$ isn't in the form $(x+a)^2+b$, 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

Why do you think it's wrong? It looks right to me.

So if $(x-3)^2+9=(x+a)^2+b$ 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) ?????

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.

i really dont know please help

Well what writing the coordinate (p,q) means is that x=p and y=q.

What happens when you evaluate $y=(x-3)^2+9$ when $x=-3,y=9$? What about when $x=3,y=9$?

What about if you just put $x=3$ or $x=-3$ 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) ??????????

Are you guessing or are you following my guidance?

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.