how can I figure out the formula. example. I need to transform the following equation y = x2 + 4 - 8 into vertex form and then I need to state the coordinates of the vertex of the parabola. I forgot how to arrive at the answer

Answer 1

I will assume there is a typo and you meant
y = x^2 + 4x - 8

take 1/2 the coefficient of the x term, square it, then add and then subtract it
( 1/2 of 4 is 2 and then squared would be 4)

y = x^2 + 4x + 4 - 4 - 8

the first three terms are now a perfect square
y = (x+2)^2 - 12

compare this with
y = a(x-p)^2 + q which has vertex (p,q) and you can conclude that the vertex of
y = (x+2)^2 - 12 is (-2,-12)