Question

Choose the function that shows the correct transformation of the quadratic function shifted eight units to the left and one unit down. A. f(x)=(x-8)^2-1 B. f(x)=(x-8)^2+1 C. f(x)=(x+8)^2-1 D. f(x)=(x+8)^2+1

Answer 1

Answer:

The answer is. C. $f(x)=(x+8)^2-1$

Step-by-step explanation:

If we have a function f(x) then we can move its graph horizontally making the transformation $y = f(x + c)$

Then if $c> 0$ the graph will move c units to the left.

If $c$ the graph will move c units to the right.

If we apply the transformation $y = f(x) + h$ then the graph of f(x) will move vertically h units.

If $h> 0$ the displacement will be h units up

If $h$ the displacement will be h units down.

In this problem we have the parent function $y = x ^ 2$ and we want to move 8 units to the left and 1 unit to the bottom.

Then we apply the transformations described above with $c = 8$.

$y = f(x + 8) = (x + 8) ^ 2$

Now we must move the function 1 unit down, with $h = -1$.

$y = f(x + 8) -1 = (x + 8) ^ 2 -1$

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

The correct answer is option C