Question

A parabola opening down the vertex is (3,0) and passes through (12,-12) what is that written in vertex form?

Answer 1

`\large\boxed{y=-(4)/(27)(x-3)^2}`

Explanation:

The vertex form of na equation of a parabola:

`y=a(x-h)^2+k`

We have the vertex (3, 0). Substitute:

`y=a(x-3)^2+0=a(x-3)^2`

A parabola passes through (12, -12). Put the coordinates of the point to the equation and solve for a:

`-12=a(12-3)^2`

`-12=a(9)^2`

`-12=81a` divide both sides by 81

`-(12)/(81)=a\\\\a=-(4)/(27)`

Finally:

`y=-(4)/(27)(x-3)^2`