For two figures to be considered congruent, their corresponding sides and angles must all be the same. Congruence can occur in any geometric figures, from simple line segments to complicated shapes with many sides and angles. Here’s another way to think about congruence: if you cut two figures out of paper, you could place one cutout on top of the other cutout and it would disappear. Consider that geometric figures are made up of an infinite number of points. When superimposed on top of each other, all of the points in one figure would match up with all of the points in the other figure. According to the passage, which of the following is not true?

A
Paper cutouts can be used to determine congruence.

B
Congruent figures have exactly the same size and shape.

C
Congruence only happens in three- or four-sided figures.

D
Two octagons can be congruent if their corresponding sides and angles match up.

C. Congruence only happens to three- or four-sided figures.

Step-by-step explanation:

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