Question

Enter a function, g(x), to describe the graph of the function f(x) = 5x2 − 2 translated 3 units down.

Answer 1

`5x^(2) -5`

Explanation:

Vertical translation of a function is achieved by adding or subtracting a number from the function.

1. Addition indicates upward translation
2. Subtraction indicates downward translation

So, to translate g(x) 3 units down, we need to subtract 3 from g(x) as shown:

g(x) - 3

Using the value of g(x) in above expression we get:

`5x^(2) -2-3\\\\ =5x^(2) -5`

Therefore, the graph of g(x) shifted 3 units down will be
`5x^(2) -5`