Question

What is the vertex of funtion of 2x^ + 4x +1

Answer 1

The vertex form:

`f(x)=ax^2+bx+c=a(x-h)^2+k\\\\h=(-b)/(2a),\ k=f(h)`

We have

`f(x)=2x^2+4x+1\\\\a=2,\ b=4,\ c=1\\\\h=(-4)/(2(2))=(-4)/(4)=-1\\\\k=f(-1)=2(-1)^2+4(-1)+1=2(1)-4+1=2-4+1=-1`

`f(x)=2(x-(-1))^2+(-1)`

Answer:
`\boxed{f(x)=2(x+1)^2-1}`