Question

7. Which two equations are equivalent?

Answer 1

Answer:

C. $y=(x-3)^2$ and $y=x^2-6x+9$

Step-by-step explanation:

before answering the problem let us remind the formula for square of sum and differences

$(a+b)^2=a^2+2 \times a \times b + b^2$

$(a-b)^2=a^2-2 \times a \times b + b^2$

We are going to use the above two formulas to solve each part and come to an answer

A. $y = (x + 3)^2$

$(x + 3)^2=x^2+2 \times x \times 3 + 3^2$

$(x + 3)^2=x^2+6x+9$

Hence this option is not correct pair

B. $y = (x-5)^2$

$(x - 5)^2=x^2-2 \times x \times 5 + 5^2$

$(x -5)^2=x^2-10x+25$

Hence this option is also not correct pair

C. $y = (x -3)^2$

$(x - 3)^2=x^2-2 \times x \times 3 + 3^2$

$(x -3)^2=x^2-6x+9$

Hence this option is correct as it have equivalent pair

D. $y = (x + 5)^2$

$(x + 5)^2=x^2+2 \times x \times 5 + 5^2$

$(x + 5)^2=x^2+10x+25$

Hence this option is also not correct pair