Functions f(x) and g(x) are shown below.

f(x) = x^2
g(x) = x^2 + 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?

Left by 4 units

Right by 4 units

Left by 8 units

Right by 8 units

I'm pretty sure it goes to the right, but I don't know by how many units.

Question

Functions f(x) and g(x) are shown below.

f(x) = x^2
g(x) = x^2 + 8x + 16

In which direction and by how many units should f(x) be shifted to obtain g(x)?

Left by 4 units

Right by 4 units

Left by 8 units

Right by 8 units

I'm pretty sure it goes to the right, but I don't know by how many units.

solomonzelman · Answer

$$ x^2 + 8x + 16=(x+4)^2$$

hero · Answer

Hint:

Rewrite g(x) in the form (x + a)^2

lena772 · Answer

So to the right by 4 units?

hero · Answer

https://www.desmos.com/calculator/zusohpa2hc

lena772 · Answer

why does it go left if it is increasing

hero · Answer

Because what you see is an illusion:
(x + 4)^2 = (x - (-4))^2

You re-write the expression in the form on the RHS to see which way the graph has shifted. -4 means "4 units to the left"