we have that
the quadratic formula is of the form
Ax^2+Bx+C=0 ------> that is the standard form of the quadratic equation
A quadratic equation can be written in vertex form
so
y=a(x-h)^2+k
where
(h,k) is the vertex of the quadratic equation
a is the leading coefficient
To convert vertex form to the standard equation
step 1
y=a(x-h)^2+k
y=a(x^2-2hx+h^2)+k
y=ax^2-2ahx+ah^2+k
group terms
y=ax^2-2ahx+(ah^2+k)
equate to zero
ax^2-2ahx+(ah^2+k)=0
where
the coefficients A, B and C are
A=a
B=-2ah
C=ah^2+k
therefore
To convert a quadratic equation in vertex form to standard form, apply the formula above