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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
