How do you convert factored form to vertex form

We can convert factored form to vertex form by dividing the numerator by denominator.

Example -

5/2 = 2.5

Complete the squaer on that side

example

y=2x^2-28x+102

first, make value of coefient in front of x^2 term 1

factor out 2 from x^2 and x term

y=2 (x^2-14x) + 102

compete the square (take 1/2 of b and square it and add to inside of parenthasees, add negative an possitive to basicaly add zero

-14/2=-7

(-7) ^2=49

y=2 (x^2-14x+49-49) + 102

complete the square

y=2 ((x-7) ^2-49) + 102

distribute

y=2 (x-7) ^2-98+102

y=2 (x-7) ^2+4