Question

What is the vertex form of `y=4x^2+4x+1`?

Answer 1

Vertex form of equation is `y = 4(x+ 0.5)^2+0`

Explanation:

`y = 4x^2 +4x+1 or y = 4(x^2 +x) +1`

`y = 4(x^2 +x + 0.5^2) -1+1; [4*0.5^2=1]` or

`y = 4(x+ 0.5)^2+0` . Comparing with vertex form of equation

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

`h=-0.5 and k= 0` . So vertex is at `(-0.5,0)` and

vertex form of equation is `y = 4(x+ 0.5)^2+0` [Ans]