Question

What is the vertex form of `y=-1/3(x-3)(x/3+7)`?

Answer 1

Vertex form of equation is `y=-1/9(x+9)^2+16` and vertex is `(-9,16)`

Explanation:

Vertex form of equation is `y=a(x- h)^2+k`, whose vertex is `(h,k)`. Hence

`y=-1/3(x-3)(x/3+7)`

= `-1/9(x-3)(x+21)`

= `-1/9(x^2-3x+21x-63)`

= `-1/9(x^2+18x+81-81-63)`

= `-1/9((x+9)^2-144)`

= `-1/9(x+9)^2+16`

and vertex is `(-9,16)`

graph{ -1/9(x+9)^2+16 [-19, 1, 8, 18]}