1. ## Function problem

Let f(x) = x^2 and g(x)= 2x^2-4x+5.

(a) Show that g(x)= 2f(x-1)+3. [HINT: Complete the square]

(b) Explain how the graphs of f and g are related.

I did a problem similar to this but Im not sure if I solve it the same way. It was perodic problem that I did but I don't know what this problem's period is if there is one

2. Originally Posted by asweet1
Let f(x) = x^2 and g(x)= 2x^2-4x+5.

(a) Show that g(x)= 2f(x-1)+3. [HINT: Complete the square]

(b) Explain how the graphs of f and g are related.

I did a problem similar to this but Im not sure if I solve it the same way. It was perodic problem that I did but I don't know what this problem's period is if there is one
$
2x^2-4x+5 =
$

$2(x^2-2x+1) + 3 =$

$2(x-1)^2 + 3$

g is a transformation of f ... vertical stretch by a factor of 2, horizontal shift right 1, and a vertical shift up 3.