Question

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

Answer 1

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
$\frac{a}{2}=\frac{a}{2}$, $(\frac{a}{2})^2=\frac{a^2}{4}$
add positive and negative of it inside the parentesees
$y=1(x^2+ax+\frac{a^2}{4}-\frac{a^2}{4})$
factor perfect square
$y=1((x+\frac{a}{2})^2-\frac{a^2}{4})$
distribute
$y=1(x+\frac{a}{2})^2-\frac{a^2}{4}$


so invertex form, it is
$y=1(x+\frac{a}{2})^2-\frac{a^2}{4}$ or
the vertex is $(\frac{-a}{2},\frac{-a^2}{4})$