Question

I need help with this math question. The question and answers are in the picture.

Answer 1

Answer: f(x)=x^2+2x+1 and g(x)=-x^2+1 ==> 1st option

Step-by-step explanation:

Both are quadratic equations: -x^2 or x^2

Blue graph: x^2 since it's facing up

f(x)=(x-b)^2

Vertex: When x=-1, y=0 ==> 0=(-1+b)^2

0=-1+b

b=1

f(x)=(x+1)^2

f(x)=(x+1)(x+1)

f(x)=x^2+x+x+1

f(x)=x^2+2x+1

Red graph: -x^2 since it's facing down

g(x)=-x^2+b

Vertex: When x=0, y=1 ==> 1=(0)^2+b

1=0+b

b=1

g(x)=-x^2+1

f(x)=x^2+2x+1 and g(x)=-x^2+1 ==> 1st option