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

Answer 1

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.