Answer:
C. [tex]y=(x-3)^2[/tex] and [tex]y=x^2-6x+9[/tex]
Step-by-step explanation:
before answering the problem let us remind the formula for square of sum and differences
[tex](a+b)^2=a^2+2 \times a \times b + b^2[/tex]
[tex](a-b)^2=a^2-2 \times a \times b + b^2[/tex]
We are going to use the above two formulas to solve each part and come to an answer
A. [tex]y = (x + 3)^2[/tex]
[tex](x + 3)^2=x^2+2 \times x \times 3 + 3^2[/tex]
[tex](x + 3)^2=x^2+6x+9[/tex]
Hence this option is not correct pair
B. [tex]y = (x-5)^2[/tex]
[tex](x - 5)^2=x^2-2 \times x \times 5 + 5^2[/tex]
[tex](x -5)^2=x^2-10x+25[/tex]
Hence this option is also not correct pair
C. [tex]y = (x -3)^2[/tex]
[tex](x - 3)^2=x^2-2 \times x \times 3 + 3^2[/tex]
[tex](x -3)^2=x^2-6x+9[/tex]
Hence this option is correct as it have equivalent pair
D. [tex]y = (x + 5)^2[/tex]
[tex](x + 5)^2=x^2+2 \times x \times 5 + 5^2[/tex]
[tex](x + 5)^2=x^2+10x+25[/tex]
Hence this option is also not correct pair
