for the function in standard form: f(x)= x^2-2x+1

Question

a) what are the coordinates of the vertex of the parabola?  (hint: x= -b / 2a) 

 

 

 

 

 

B) is the vertex a minimum of a maximun? explain

Answer 1

Since the function can be factored and is a perfect square being f(x)=(x-1)^2. This implies the vertex is (1,0). Note: One can have a tendency to make problems like this more complicated than it is. The formula for x=-b/2a does check for determining the x coordinate of the vertex.

 

Since the coefficient of x^2 term is greater than zero, then the parabola opens up and the vertex is the minimum value of the function.