Question

7. Which two equations are equivalent?

A. y = (x + 3)2 and y = x2 + 6
B. y = (x – 5)2 and y = x2 – 25
c. y = (x – 3)2 and y = x2 - 6x + 9
D. y = (x + 5)2 and y = x2 + 25x + 10

Answer 1

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

Explanation:

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

`(a+b)^2=a^2+2 * a * b + b^2`

`(a-b)^2=a^2-2 * a * 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 * x * 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 * x * 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 * x * 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 * x * 5 + 5^2`

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

Hence this option is also not correct pair