Question

Choose the function that shows the correct transformation of the quadratic function shifted eight units to the right and one unit down. ƒ(x) = (x - 8)2 - 1 ƒ(x) = (x - 8)2 + 1 ƒ(x) = (x + 8)2 - 1 ƒ(x) = (x + 8)2 + 1

Answer 1

You need to substitute x=x-8 to move it towards right and y=y+1 to move it downwards.

Hence, the answer would be f(x)=(x-8)2+1

Answer 2

The correct option is 1.

Explanation:

The parent quadratic function is

`g(x)=x^2`

The transformation of the quadratic function is defined as

`f(x)=(x+a)^2+b` .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph of function shifts a units left and if a<0, then the graph of function shifts a units right.

If b>0, then the graph of function shifts b units up and if b<0, then the graph of function shifts b units down.

It is given that the quadratic function shifted eight units to the right and one unit down. It means a=-8 and b=-1.

Substitute a=-8 and b=-1 in equation (1).

`f(x)=(x+(-8))^2+(-1)`

`f(x)=(x-8)^2-1`

Therefore the correct option is 1.