Question

Choose the function that shows the correct transformation of the quadratic function shifted eight units to the left 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

The vector[-8;-1]


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


:)

Answer 2

The correct option is 3.

Explanation:

The parent quadratic function shifted is

`f(x)=x^2`

The translation 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 shifts a units left and if a<0, then the graph shifts a units right.

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

It is given that the quadratic function shifted 8 units left and 1 units 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 3.