x = -3 and x = 5 are roots.....and ( 1, -6) is on the graph.....so.......we have this
-6 = a(1+3) (1 - 5) simplify
-6 = a (4) ( - 4)
-6 = (-16)a
a = -6/-16 = 3/8
So......the function is
f(x) = (3/8) ( x + 3) ( x - 5)
f(x) = (3/8) ( x^2 -2x - 15)
f(x) = (3/8)x^2 - (3/4)x - 45/8
See the graph here : https://www.desmos.com/calculator/aqoish07nx