Question

How do you write the equation of the parabola in vertex form given vertex is at (-1, 17) and the parabola passes through the point (0, 6)?

Answer 1

`y = - 11 (x + 1 )^2 + 17`

Explanation:

The equation of a parabola in vertex form is

`y = a(x - h )^2 + k`
`" where (h , k) are the coordinates of vertex "`

here the vertex = (-1 , 17 ) and so equation is

`y = a(x + 1 )^2 + 17`

Since the point (0 , 6) lies on the parabola it will satisfy the equation and by substituting the coordinate point , will allow a to be found.

hence `6 = a(0+1)^2 + 17 → 6 = a +17 → a = - 11`

`rArr y = -11(x + 1 )^2 + 17`