Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.
-Shift 66 units to the left and 72 units down.
A) $f ( x ) = ( x - 66 ) ^ { 2 } - 72$
B) $f ( x ) = ( x - 72 ) ^ { 2 } - 66$
C) $f ( x ) = ( x + 66 ) ^ { 2 } - 72$
D) $f ( x ) = ( x - 72 ) ^ { 2 } + 66$

Question

Determine a quadratic function that results when applying the given shifts to the graph of f(x) = x2.
-Shift 66 units to the left and 72 units down. 
A) $f ( x ) = ( x - 66 ) ^ { 2 } - 72$
B) $f ( x ) = ( x - 72 ) ^ { 2 } - 66$
C) $f ( x ) = ( x + 66 ) ^ { 2 } - 72$
D) $f ( x ) = ( x - 72 ) ^ { 2 } + 66$

Quizplus · Accepted Answer

To shift 66 units to the left and 72 units down, we need to use the form:
$f(x-a) + b$
where a is the amount of shift to the right/left and b is the amount of shift up/down.

Plugging in the values for a and b, we get:
$f(x+(-66))+(-72)$
Simplifying, we get:
$f(x-66)-72$
Now, we need to square the expression inside the function to get the quadratic form:
$f(x-66)^2-72$
Therefore, the quadratic function resulting from the given shifts is:
$f(x) = (x+66)^2-72$, which is equivalent to choice C.

Determine a Quadratic Function That Results When Applying the Given f(x)=(x−66)2−72f ( x ) = ( x - 66 ) ^ { 2 } - 72f(x)=(x−66)2−72

Determine a Quadratic Function That Results When Applying the Given $f ( x ) = ( x - 66 ) ^ { 2 } - 72$