a] Vertex form
Vertex form is given by:
y=(x-h)²+h0
where:
(h,k) is the vertex
Given that:
f(x)=x²-6x+13
The vertex will be evaluated as follows:
c=(b/2a)²
b=-6
thus
c=(-6/2*1)²=9
hence adding and subtracting 9 in the expression we get:
f(x)=x²-6x+9-9+13
f(x)=x²-6x+9+4
writing the above in vertex form we get
f(x)=(x-3)²+4
b] The minimum value of f(x) is at it's vertex. Thus from the function
f(x)=(x-3)²+4
the vertex is at (3,4)
hence the minimum value is at (3,4)
