Respuesta :
The function [tex]f(x) = x^2-6x+1[/tex] is an order 2 function. To make it to the perfect square, 8 units of tiles are added to the function.
Option C is correct.
What is a function?
The function can be defined as an expression that defines a relationship between one independent variable with another dependent variable.
The given function is [tex]f(x) = x^2-6x+1[/tex].
The function needed more unit tiles to add so that it becomes a complete square.
The given function is an order 2 function, the side of the square will be order 1. Let's consider an order 1 function ax+b to be the side of the square. Also, consider that t number of tiles added to the order 2 function so that it can become the perfect square.
[tex]f(x) + t = (ax+b)^2[/tex]
[tex]x^2 -6x + 1 + t = a^2x^2 + 2abx + b^2[/tex]
By comparing the integers of both sides of orders, we get
[tex]a^2=1, \;2ab = -6, \; b^2 = 1+t[/tex]
Putting the value of a to get the value of b,
[tex]2\times 1 \times b = -6\\b=-3[/tex]
The value of t can be found out as,
[tex](-3)^2 = 1+t\\9 = 1+t\\t=8[/tex]
Hence we can conclude that 8 units of tiles are added to make the function, a perfect square.
To know more about the function, follow the link given below.
https://brainly.com/question/14218786.
