EmilyJernigan 3 years ago The function f(x) = x2. The graph of g(x) is f(x) translated to the left 6 units and down 5 units. What is the function rule for g(x)? A. g(x) = (x + 6)2 - 5 B. g(x) = (x - 5)2 + 6 C. g(x) = (x - 6)2 + 5 D. g(x) = (x + 5)2 - 6

1. Calcmathlete

The form that you need to use here is: \[g(x) = (x - h)^2 + k\]Where h = -6 and k = -5 Can you simplify to find your answer?

2. EmilyJernigan

umm... no. ha. i have no clue how to do it

3. Calcmathlete

Alright. I can walk you through it then :) First of all, do you get how I got -6 for h? When you think about it, if you were to go the the right by 6, you would get h = 6 since going to the right is generally thought of as a positive direction. However, since it's going to the left by 6, it's h = -6 since left is a negative direction. Same for the k part. It moves down by 5 which is a negative direction. Now you just plug in numbers.

4. Calcmathlete

Now, just substitute in what you have for h and k in order to finish up. \[y = (x - (-6))^2 + - 5 \implies ?\]You have to think. A negative times a negative is a positive. A negative times a positive is a negative. So, it would become: \[y = (x + 6)^2 - 5\]Do you get it?

5. EmilyJernigan

yeah. but i dont understand how thats gonna get me my ansswer

6. alexwee123

@EmilyJernigan he just gave you the answer :D

7. EmilyJernigan

He has two as an exponent or whatever. but thats not on any of my answers

8. Calcmathlete

It was just a fail in the copy and paste. When you copy and paste problems, the exponent does not maintain the exponent size, but rather becomes a regular number, so the 2 after the parentheses are meant to be exponents.