Question

What is the parent function for the following

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

Answer 1

The parent function of f(x) = (x-2) (x-1) is
`P(x) = x^2- 3 x + 2`.

Explanation:

Here, f(x) = (x-2) (x-1)

Now, parent function of a given function is the function, which is PRODUCT OF ALL IT S FACTORS.

Now, here, f(x) has two factors ( x- 2) and ( x-1)

So, the parent function p(x) of f(x) is given as the product of both the factors.

So, we get:

`P(x)  = (x-2) (x-1) \\=  x( x-1) -2(x-1)\\=x^2 - x -2x + 2\\= x^2- 3 x + 2\\\implies P(x) = x^2- 3 x + 2`

Hence, here the parent function of f(x) = (x-2) (x-1) is
`P(x) = x^2- 3 x + 2`.