Question

How do you rewrite `f(x) = 2(x-1)^2+3` from vertex form to standard form?

Answer 1

`f(x)=2x^2-4x+5`

Explanation:

The equation is already in vertex form i.e. `f(x)=a(x-h)^2+k`, with `(h,k)` as vertex. Here we have vertex as `(1,3)`.

Standard form of equation is `f(x)-av^2+bx+c` and for this we just need to expand RHS, which can be done as follows:

`f(x)=2(x-1)^2+3`

= `2(x^2-2x+1)+3`

= `2x^2-4x+2+3`

= `2x^2-4x+5`