Write the quadratic function y = x2 + ax (assuming a is nonzero) in vertex form.

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
,
add positive and negative of it inside the parentesees

factor perfect square

distribute


so invertex form, it is
or
the vertex is