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

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

geerky42 · Answer

Well you need to rewrite $g(x)$ in form of $(x-h)^2 + k$

Note that $g(x)$ is already completed square so we have $g(x) = (x + 4)^2$

So $h = -4$ which mean $g(x)$ is $f(x)$ shifted 4 units left.