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)
