Question

Write the equation of the parabola in vertex form. vertex (3,2), point (2,-4) f(x)=

Answer 1

The equation of the parabola in vertex form

$y=-6(x-3)^2+2$

Given :

vertex (3,2), point (2,-4)

The vertex form of parabola is $y=a(x-h)^2+k$

Where (h,k) is the vertex

Given vertex is (3,2). so, h=3 and k=2

Replace it in the equation

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

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'

$y=a(x-3)^2+2\\-4=a(2-3)^2+2\\-4=a(1)+2\\-4=a+2\\-4-2=a\\a=-6$

the equation of the parabola in vertex form

$y=-6(x-3)^2+2$

Learn more : brainly.com/question/9030390