Question

8.
How many units and in what direction will the function g(x) = (x + 5)2 - 9 translate if the parent function is f(x) = x2?


A. 9 units to the left 5 units down
B. 9 units to the left 5 units up
C. 5 units to the left and 9 units down
D. 5 units to the left and 9 units up

Answer 1

We need to deal with a translation in x (horizontal translation) and a translation in y (vertical translation.)

Let's start with the translation in x.

When you replace x by x - k, the function moves k units along the x axis (right or left). If k is positive, it moves right. If k is negative, it moves left.

For the translation in x (the horizontal translation), you are comparing \(x^2\) with \((x + 5)^2\).

Write x + 5 as x - k.
What is k?

Answer 2

k isnegative @mathstudent55

Answer 3

Correct.
x + 5 = x - (-5) = x - k, so
k = -5, so this means a translation of 5 units to the left.

Answer 4

Now we need to deal with the vertical translation.

Answer 5

Think of

\(g(x) = (x + 5)^2 - 9\)

as

\(y = (x + 5)^2 - 9 \)

Now add 9 to both sides:

\(y + 9 = (x + 5)^2 \)

A similar rule applies to y.
If you replace y by y - h, the function has a translation of h units vertically.
It translates up for positive h and down for negative h.

Here y was replaced by y + 9.
Now express y + 9 as y - h.
What is h?

Answer 6

nine is also negative @mathstudent55

Answer 7

Correct. That means 9 units down.