we know that
for
y=a(x-h)^2+k
vertex is (h,k)
given vertex is (3,5)
y=a(x-3)^2+5
we are also given
(5,-3)
x=5 and y=-3 is a possible solution
-3=a(5-3)^2+5
-3=a(2)^2+5
minus 5 both sides
-8=a(4)
-8=4a
divide by 4 both sides
-2=a
the equation is
[tex]y=-2(x-3)^2+5[/tex]
