Question

How do you determine the equation of the parabola with vertex (2,6) and passes through (7,2)?

Answer 1

`y=-4/25(x-2)^2+6`

Explanation:

The equation of a parabola in `color(blue)"vertex form"` is

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=a(x-h)^2+k)color(white)(a/a)|)))`
where (h ,k) are the coordinates of the vertex and a, a constant.

here (h ,k) = (2 ,6)

`rArry=a(x-2)^2+6 " is the partial equation"`

Given that the parabola passes through (7 ,2) then the coordinates of this point will satisfy the equation.
Substituting x = 7 and y = 2 into the equation allows the constant a to be found.

`rArra(7-2)^2+6=2rArr25a=-4rArra=-4/25`

`rArry=-4/25(x-2)^2+6" is the equation in vertex form"`