Question

How do you find the vertex of `y= x ^ { 2} + 6x - 16` by completing the square?

Answer 1

Vertex is at `(-3, -25)`

Explanation:

`y = x^2+6x -16 = x^2+6x +3^2 -9 -16 = (x+3)^2 -25`

Comparing with standard vertex form of equation

`y = a (x-h)^2 +k ; (h,k)` being vertex , we find here

`h= -3 , k= -25`. So vertex is at `(-3, -25)`

graph{x^2+6x-16 [-80, 80, -40, 40]} [Ans]