get into form y=a(x-h)²+k where (h,k) is vertex
some terms:
quadratic coefient: number in front of the x² term
linear coefient: number in front of the x term
basically complete the square
so
y=x²+ax
first factor out the quadratic coefient (1),
y=1(x²+ax)
take 1/2 of the linear coefient and square it
[tex]\frac{a}{2}=\frac{a}{2}[/tex], [tex](\frac{a}{2})^2=\frac{a^2}{4}[/tex]
add positive and negative of it inside the parentesees
[tex]y=1(x^2+ax+\frac{a^2}{4}-\frac{a^2}{4})[/tex]
factor perfect square
[tex]y=1((x+\frac{a}{2})^2-\frac{a^2}{4})[/tex]
distribute
[tex]y=1(x+\frac{a}{2})^2-\frac{a^2}{4}[/tex]
so invertex form, it is
[tex]y=1(x+\frac{a}{2})^2-\frac{a^2}{4}[/tex] or
the vertex is [tex](\frac{-a}{2},\frac{-a^2}{4})[/tex]
