Question

Let f(x)=2x2−1.

The quadratic function g(x) is f(x) translated left 2 units.
Enter the equation of g(x) in the box.

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Answer 1

`g(x) = 2(x+2)^2 -1`

Explanation:

In general if a function f translated a units left i,e

y =f(x) translated by a units left we have;

y =f(x+a)

Given the function:

`f(x) = 2x^2-1`

We have to find the function g(x):

g(x) is f(x) translated left 2 units

By definition we have;

⇒
`g(x) = f(x+2)`

⇒
`g(x) = 2(x+2)^2 -1`

Therefore, the equation of g(x) is,

`g(x) = 2(x+2)^2 -1`

Answer 2

f(x)=2x^2 -1
Translation is a function transformation that transform the function in a way of translating. By translating the function its graph is moved up an down. Moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1