Question

How do you write the equation of the parabola in vertex form given vertex (3, -3) point (0, 6)?

Answer 1

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

Explanation:

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

where (h , k ) are the coordinates of the vertex. Here (3 , -3)

hence equation is `y = a(x - 3 )^2 - 3`

To find the value of a , substitute (0 , 6 ) into the equation.

so `a(0-3)^2 - 3 = 6 → 9a - 3 = 6 → 9a = 9 → a = 1`

`rArr y = (x - 3)^2 - 3 " is the equation in vertex form "`