Question

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

Answer 1

See explanation.

Explanation:

The vertex form of a quadratic function is:

`f(x)=a(x-p)^2+q`

where

`p=(-b)/(2a)`

and

`q=(-Delta)/(4a)`

where

`Delta=b^2-4ac`

In the given example we have:

`a=-1`, `b=4`, `c=1`

So:

`p=(-4)/(2*(-1))=2`

`Delta=4^2-4*(-1)*1=16+4=20`

`q=(-20)/(-4)=5`

Finally the vertex form is:

`f(x)=-(x-2)^2+5`