Function 1:
The quadratic function is given as:
[tex]f(x)=2x^2-8x+1[/tex]
Factor out 2:
[tex]f(x)=2(x^2-4x)+1[/tex]
Rewrite the expression in the bracket, as follows:
[tex]f(x)=2(x^2-4x+4-4)+1[/tex]
This gives:
[tex]\begin{gathered} f(x)=2(x^2-4x+4)-8+1 \\ f(x)=2(x^2-4x+4)-7 \end{gathered}[/tex]
Express as a perfect square:
[tex]f(x)=2(x-2)^2-7[/tex]
A quadratic function is represented as:
[tex]f(x)=a(x-h)^2+k[/tex]
Where: vertex (h,k)
By comparison, we have:
Vertex = (2, -7)
This represents the minimum of function 1.
Function 2:
From the graph, the minimum of function 2 is:
Vertex = (-1, -3)
(2,-7) is lesser than (-1,-3)
Answer: Function 1 has the least minimum value at a coordinate of (2,-7)
