Question

Find the vertex of the parabola
y= x^2-2x-1
vertex (?,?)

Answer 1

`y=a(x-h)^2+k \Rightarrow \hbox{vertex}=(h,k)\\\\ y=x^2-2x-1\\ y=x^2-2x+1-2\\ y=(x-1)^2-2 \Rightarrow \hbox{vertex}=(1,-2)`

Answer 2

`y=ax^2+bx+c\\\\vertex:(x_v;\ y_v)\\\\x_v=(-b)/(2a)\ and\ y_v=f(x_v)`



`y=x^2-2x-1\\\\a=1;\ b=-2;\ c=-1\\\\x_v=(-(-2))/(2\cdot1)=(2)/(2)=1\\\\y_v=1^2-2\cdot1-1=1-2-1=-2\\\\Answer:(1;-2)`