If the gcf of two numbers is 9, why must both numbers be a multiple of 9?

Okay, so I've thought about it and now I think I know what the question means.

GCF of 2 numbers means that 2 numbers share the same Greatest Common Factor.  That said, since we know the greatest common factor, we need to multiply 9 to get those 2 numbers.

9 X 1 = 9
9 X 2 = 18
9 X 3 = 27
9 X 4 = 36
9 X 5 = 45

These are the only multiples you need to figure out the rest.

9 X 1 is unnecessary when we look at multiples and factors because it is just the same number to finish.
9 X 4 isn't helpful because large even numbers can just be divided by 2 to get the GCF. (It isn't 9)
9 X 5 can be divided by 15, which makes 15 the GCF rather than 9.

So that leaves us with 9 X 2 and 9 X 3.  But we're not done yet.

Why must both numbers be a multiple of 9?

Simply because in order to get to the numbers in the first place, you have to multiply by nine.  So a way to check your work for this is to multiply 9 X 2, and then divide by 9 again to make sure that it is a real number.  That sounds really complicated, but it's beyond simple when you look at it like this:

9 X 2 = 18
18 / 9 = 2

And there ya go!  Hope this helps.

Idon't see any graph, however the graph of the function : f(x) = x²-2x+3 is a parabola: 1) open upward (since a> 0)2) it intersects y-axis in 3 (y=3)3) its axis of symmetry is x = +1 ( -b/2a)4) it's minimum is y = -2, so its vertex is (1,-2)5) it doesn't intersect the x-axis since discriminant < 0