In the diagram, ce = 12 and be = 5.

based on the given information, ae =

12 units

Step-by-step explanation:

From the given figure, it can be seen that AB=BC, thus

From ΔBEC, using the Pythagoras theorem, we have

Now, from ΔABE, using the Pythagoras theorem, we have

Thus, the measure of AE is 12 units.

we know that

AB=BC ------> given problem

Step

In the right triangle BCE

Find the value of BC

Applying the Pythagorean Theorem

in this problem we have

substitute the values

Step

In the right triangle ABE

Find the value of AE

Applying the Pythagorean Theorem

in this problem we have

substitute the values

therefore

the answer is

The length of side AE is

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