Question

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

Answer 1

`y=-4(x-3)^2+2`

Explanation:

`y=a(x-p)^2+q` - equation of the parabola in vertex form

from vertex (3,2) we know that
`p=3, \ q=2`

from point (2,-2) we know that
`x=2, \ y=-2`

inserting p=3, q=2, x=2 and y=-2 to the equation
`y=a(x-p)^2+q`, we calculate
`a`

`-2=a(2-3)^2+2\\ -2=a\cdot(-1)^2+2\\ -2=a\cdot1+2\\ -2=a+2\\ -2-2=a\\ -4=a\\ a=-4`

insert a=-4, p=3 and q=2 to the equation

`y=-4(x-3)^2+2`