Question

Choose the function that correctly identifies the transformation of f(x) = x2 shifted four units right and seven units down.

g(x) = (x - 4)2 - 7
g(x) = (x - 4)2 + 7
g(x) = (x + 4)2 + 7
g(x) = (x + 4)2 - 7

Answer 1

g(x) = (x - 4)2 - 7


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Answer 2

Answer:

The correct option is A.

Step-by-step explanation:

The parent quadratic function is,

$f(x)=x^2$

The transformation is defined as

$g(x)=(x+a)^2+b$       ....(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 f(x) shifted four units right and seven units down. It means a=-4 and b=-7.

Substitute a=-4 and b=-7 in equation (1).

$g(x)=(x-4)^2-7$

The required function is $g(x)=(x-4)^2-7$.

Therefore the correct option is A.