Question

What is the vertex form of `y=x^2+45x+31` ?

Answer 1

Vertex form of equation is `y= (x+22.5)^2 - 475.25`

Explanation:

`y = x^2+45x+31 or y = x^2 + 45x +(45/2)^2 - (45/2)^2 +31`

`y= (x+45/2)^2 -2025/4 +31 or y= (x+45/2)^2 - 1901/4` or

`y= (x+22.5)^2 - 475.25` . Comparing with vertex form of

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

`h= -22.5 , k = -475.25 :.` Vertex is at `( -22.5 ,-475.25)`

and vertex form of equation is `y= (x+22.5)^2 - 475.25` [Ans]