Question

What is the vertex of f(x)=x^2-6x+3

Answer 1

Rearrange into vertex form

x^2 - 6x + 3

= (x - 3)^2 - 9 + 3

= (x - 3)^2 - 6

This is vertex form ( y = a(x - b)^2 + c is general vertex form with vertex

= (b, c) ).

So here the vertex is (3, -6) answer

Answer 2

`f(x)=ax^2+bx+c\\\\\text{the vertex}\\\\V(h,\ k)\\\\h=(-b)/(2a),\ k=f(h)`

We have:

`f(x)=x^2-6x+3\\\\a=1,\ b=-6,\ c=3\\\\h=(-(-6))/(2(1))=(6)/(2)=3\\\\k=f(3)=3^2-6(3)+3=9-18+3=-6`

Answer: (3, -6)