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?

A. the correct factored form is y=(x+4)^2. this shifts the graph of y=x^2 up 4 units.

B. the correct factored form is y=(x+4)^2. this shifts the graph of y=x^2 right 4 units.

C. the correct factored form is y=(x+4)^2. this shifts the graph of y=x^2 left 4 units.

D. the correct factored form is y=(x+16)^2. this shifts the graph of y=x^2 up 16 units.

E. the correct factored form is y=(x-4)(x+4). this shifts the graph of y=x^2 right 4 units and up 4 units.

Answer 1

The standard graph is y=x^2.
The shifted graph is
y=a(x-h)^2+k
which shifts the graph h units to the right, and k units up with a vertical multiplication factor a.
In the given problem,
h=-4,
k=0,
a=1.

Try to interpret the results.