Consider y=x^2+8x+16.

Question

What is the correct way to factor this equation?
How does this equation shift the graph of y=x^2?

Answer 1

The answer can be correct or incorrect.

There are many ways to solve a ,atj problem, depending on the conditions.

Any way that give a correct answer is a correct way.

Here the most obvious way to factor is to note that it is a perfect square:
x^2+8x+16
=x^2+2(4x)+4^2
=(x+4)^2

Alternatively, you could see that:
x^2+8x+16
=x^2+4x+4x+4^2
=x(x+4)+4(x+4)
=(x+4)(x+4)
=(x+4)^2
as above.

Both methods are correct, the first one is more intuitive.