Hi welcome to MooMooMath Today we are going
to talk about Quadratics and changing a quadratic
from standard form to vertex form Lets overview
quickly what standard form is.
Standard form is ax squared plus bx plus c
is equal to y and vertex is equal to a parenthesis
minus h quantity squared plus k equals y.
Those are the two forms of the quadratic.
The vertex form is handy because the hk is
your vertex and standard form is nice if you
are using the quadratic formula.
Sometimes we have to go from standard form
to vertex form . Let's learn how to do that.
Let's start with a lead coefficient of one
which is the easier one.
We have x^2 + 8x + 3 = y We want to change
this to the vertex form.
Step 1 is to group our x values together and
complete the square.so we can write the equation
as a perfect square.
I will write the x^2 and 8x together.
I will push the positive 3 to the side because
the constant 3 does not complete the square.
What we need to do is find a value that completes
the square.
I will take the value b which is the coefficient
to the linear term and half it and square
it and this will complete the square.
I will take b and half it and then square
it.
Half of 8 is 4 and 4 squared is 16.
I will put 16 back in the equation to complete
the square.
What I have completed with these three terms
is a trinomial that will factor to (x+4)^2
Next I can't just add 16 to the equation because
it will be unbalanced.
When I add 16 it is out of balance, so I have
to subtract 16 from the equation to get it
back in balance.
I will group negative 16 with constant 3 and
add these together to get -13.
What I have done is combine those two constants
together, and now we have our quadratic in
vertex form.
h is -4 and k is -13.
h is always the opposite sign of what we see
in the equation because it is x-h and k is
the same value which is -16.
The vertex 
is (-4,-13)
Let's try another 
one so you can see the pattern.
x^2 + 24x -1 = f(x)
Group the x's together x squared and 24x
push the 1 over which will become part of
my k value.
Part of the constant on the outside.
Now complete the square, take 24 and half
it and square it So half of 24 is 12 and 12
squared is 144.
We can't just 144 without subtracting 144
. Now group the first three terms together
to make our perfect square.
The perfect square it factors to is always
the square root of what we just found.
(the 144) and in the back we get negative
145 . Now we have our functions, so we can
figure out our h and k. h is the opposite
of what we see (-12) and k is the same sign
as what we see, and there is your vertex that
you can use to graph your quadratic equation.
Hope this video was helpful.
