How do you find the vertex of a parabola given only the roots and AOS?

Question

Preferably in standard form, I don’t know vertex form.

Answer 1

if you know the roots, r1 and r2

then the parabola is y=a(x-r1)(x-r2)

expand

y =a(x^2 -r1x-r2x +r1r2

y = ax^2 -a(r1+r2)x + ar1r2

standard form is y = ax^2 +bx + c

in this example

a= a

b =-a(r1+r2)

c = ar1r2