Hi, I got a question asking "Find the equation of the locus of the vertex of f(x)=x^2-2mx+2m+1 "What is locus is and how can i write an equation of a locus i made a search but didnt really get anything useful. Thanks
1. Calculate the coordinates of the vertex:
. Therefore the coordinates of the vertex are:
V(m, -m^2+2m+1)
2. From the coordinates you know:
3. Substitute the term for m from the 1rst equation into the 2nd equation. You get:
. And that's the equation of the curve on which all vertices of all parabola are placed. (Red line)