Question

How do I make an equation for this parabola knowing:

Vertex: (3,2)
y-intercept: -16
x-intercepts: 2 and 4

Answer 1

(x-h)^2=-4a(y-k) form
h=3
k=2
put the points 4,0 2,0 & 0,-16
to get the value of a

Answer 2

if your
x-intercepts: 2 and 4 then
(x-2)(x-4)=0 that is
x^2 -6x+8=0, assuming y-intercept: +16 ,then multiplying by 2 to get
2x^2 -12x+16=0 Equation of parabola
vertex v=-b/2a=-(-12)/2(2)=3 and
f(3)=3^2 -12(3)+16=-2 therefore vertex(3,-2)