Question

Let f(x)=2x2−8 .

Answer 1

Answer:

$g(x)=2x^2-10$

Step-by-step explanation:

The function f(x) is given by

$f(x)=2x^2-8$

The quadratic function g(x) is obtained by translating f(x) 2 units down.

We use the below rule to find the equation for g (x)

Rule:- If a function f(x) is translated 'c' units down then the equation of the translated function be f(x)-c

Here, f(x) is translated 2 units down to obtain g(x).

Hence, we have

$g(x)=f(x)-2\\\\g(x)=2x^2-8-2\\\\g(x)=2x^2-10$

Answer 2

Move down c units means minus 2 from whole function

f(x) moved down 2 units means f(x)-2
so

f(x)-2=2x²-8-2
f(x)-2=2x²-10


g(x)=2x²-10