Write the equation of the parabola in vertex form: the vertex is (2,3)​, and a point on the parabola is (3,−2)?

y=a(x-h)^2+k

step 1 we know vertex so we get equation

y=a(x-2)^2+3

step 2 solve for a by plugging point (3,-2)

-2=a(3-2)^2+3

-2-3=a(1)^2

-5=a

now we get the equation:

y= -5(x-2)^2 +3

and you're done

Hint:
the equation of the parabola in vertex (h,k) is y = a(x-h)^2+k