How many more unit tiles must be added to the function f(x)=x2−6x+1 in order to complete the square?
Accepted Solution
A:
8 unit tiles should be addedStep-by-step explanation: Function given is [tex]f(x)=x^{2}-6x+1[/tex]. We wish to add more unit tiles to the function so that it becomes a complete square. Since the given function is of order 2, the side of the square will be order 1. Let us assume a general order 1 expression [tex]ax+b[/tex] to be the side of the square. As the function forms the square after adding some [tex]p[/tex] unit tiles, [tex]f(x)+p=(\text{Side of square})^{2}[/tex][tex]x^{2}-6x+1+p=(ax+b)^{2}=a^{2}x^{2} +2abx+b^{2}[/tex]From comparision, [tex]a^{2}=1; 2ab=-6; b^{2}=1+p\\a=1; b=-3\\(-3)^{2}=p+1\\p=8[/tex]∴ 8 more unit tiles are required to complete the square.