The equation of the parabola in vertex form
[tex]y=-6(x-3)^2+2[/tex]
Given :
vertex (3,2), point (2,-4)
The vertex form of parabola is [tex]y=a(x-h)^2+k[/tex]
Where (h,k) is the vertex
Given vertex is (3,2). so, h=3 and k=2
Replace it in the equation
[tex]y=a(x-3)^2+2[/tex]
Now we find out the value of 'a' using the given point (2,-4)
Point (2,-4) is (x,y)
x=-2 and y=-4
Replace it in the equation we got to find out 'a'
[tex]y=a(x-3)^2+2\\-4=a(2-3)^2+2\\-4=a(1)+2\\-4=a+2\\-4-2=a\\a=-6[/tex]
the equation of the parabola in vertex form
[tex]y=-6(x-3)^2+2[/tex]
Learn more : brainly.com/question/9030390