So someone help me explain how they found the solution to this Example 2?

Step-by-step explanation:

The line segment would like something like so:

X--------------------------Y---------------------------Z

The segment addition postulate says that x------y + y-------z = x-------y--------z

You are given the following measures for each:

            5x-3                         8x-9

X--------------------------Y---------------------------Z

|______________131______________|

You now need to substitute this in for the postulate:

Simplify the equation to solve for the value of x. Remove the parentheses:

Combine like terms to simplify the equation (make sure to keep the symbol of a term the same when combining. For example, since the negative symbol is in front of the three, it will be -3):

Use inverse operations. Add 12 to both sides:

Use inverse operations to isolate the variable. Divide both sides by 13:

Now that we know the value of x, we can insert its value into each given length to simplify:

--------------------

------------------

To make sure the values are true, insert them into the postulate:

Since the equation is true:

              52                            79

X--------------------------Y---------------------------Z

|______________131______________|

:Done

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

what is the rest of the question? ?