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in this lesson we're going to talk about

how to convert a quadratic function in

standard form to vertex form and vice

versa sometimes you may need to be able

to do this so let's cover in this video

and a way to do it is to use the need to

complete a square basically half of 6 is

3 so we're going to add 3 square roots

of both sides adding it to the left side

is the same as subtracting it from the

right side so we can add 3 squared at

both sides or we can add 9 to the right

side and also simultaneously subtract 9

from the right side 9 and negative 9 is

0 so we're not changing the value at the

right side so let's do it that way now

let's factor x squared plus 6 X plus 3

squared every time you complete the

square you're creating a perfect square

trinomial and to factor it you can see

everything you need here first it's X

and then whatever this sign is it's plus

and then it's this number before you

squared 3 squared outside we have

negative 5 minus 9 so in vertex form

it's X plus 3 squared minus 14 so we can

clearly see that the vertex is negative

3 and negative 14 and we can also use

this equation to find vertex and then

get to B over 2a B is 6a a is 1 negative

6 over 2 is negative 3 which confirms

the x value here now let's talk about

how we can go back to standard form

so how can we convert this expression

which is in vertex form back to standard

form all you need to do is expand X plus

3 squared let's foil it x times X is x

squared x times 3 is 3x 3 times X is 3x

3 times 3 is 9 and then combine like

terms 3x plus 3x is 6x 9 minus 14 is

negative 5 so this gives us the original

function in standard form so now you

know how to convert from standard form

it's a vertex form by completing the

square and you know how to convert from

vertex form to standard form by

expanding and using the foil method