Question

What is the equation for `g(x)` if `g(x) = f(x) = (x-8)^2 + 10` translated 2 units up and 5 units left?

Answer 1

`g(x)=(x-3)^2+12`

Explanation:

`g(x)=(x-8)^2+10--(1)`#

is translated 5 units left, 2 units up

i.e. by the vector `((-5),(2))`

consider the vertex of `(1)`

vertex of`" "g(x)=(x-8)^2+10" "` is `(8,10)`
as seen by the graph graph{(x-8)^2+10 [-18.54, 46.4, -1.8, 30.68]}

the this coordinate will become

`(8,10)rarr((8-5),(2+10))rarr(3,12)`

the new eqn is then

`g(x)=(x-3)^2+12`

graph{(x-3)^2+12 [-27.04, 121.04, -5, 69.1]}