segment AB is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by?

As you forgot to mention the diagram. I was able to find the diagram. Hence, I am attaching and solving the question based on that diagram, which anyways would clear your concept.

we conclude that the segment AB was dilated by scale factor 3.

Step-by-step explanation:

From the diagram, it is clear that the original points A and B are located

at (0, 2) and (2, 3) respectively.

i.e.

As the coordinates of the dilated segment A'B' are given as:

A scale factor is basically a number that multiplies an object or quantity.

For instance, the 'D' in is the scale factor for x.

If the equation were y = 7x, then the factor would have been 5.

As the coordinates of the dilated segment A'(0, 6) and B'(6, 9) are 3 times the coordinates of the original segment A(0, 2) and B(2, 3).

i.e.

A(0, 2)  → (0×3, 2×3) = A'(0, 6)

B(2, 3) → (2×3, 3×3) = B'(6, 9)

Therefore, we conclude that the segment AB was dilated by scale factor 3.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1