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## Algebra 1 (Eureka Math/EngageNY)

### Course: Algebra 1 (Eureka Math/EngageNY)>Unit 4

Lesson 13: Topic C: Lessons 18-19: Translating graphs of functions

# Graphing shifted functions

Given the graph of f(x)=x², Sal graphs g(x)=(x-2)²-4, which is the graph of f shifted 2 units to the right and 4 units down.

## Want to join the conversation?

• Why does Sal move the graph 2 units to the right when it says -2 at ?

Shouldn't he move it to the left by 2 units?
• Think about it on a coordinate plane: if I shift 0 two to the right, I get 2. Because you have to think about it in terms of 0, not 2, you subtract 2 instead of adding 2.
• I wish these videos were explained better. I feel like its really brief and I still don't understand how you get to where you are by the end. I wish I could be more specific but I guess I don't understand it. There is no introduction really explaining whats going on either. Also taking the simplest explanation and then jumping to advanced problems there is no bridge.
• My favorite video about this topic is the Shifting Functions Introduction video. I love how Sal explains this concept there.
• Does the fact that the x-2 is squared change the graph? Why not?
Also, is f(x)=x the same thing as f(x)=x^2? Why or why not?
• Anyone besides me have trouble with the interactive graphs? On the quiz after "Shifting Functions" I bet I took the quiz four times to even get three out of four correct. And each time I know I had the formula for shifting graphs figured out correctly but when I graphed the functions with the interactive graphs I got each one wrong. And I believe it was a result of me not being able to set the graphs exactly right. For example, the last graph I tried the tip of the graph was 8 places to the right and one place up. And when I set the graph to that location the system still counted it wrong. In the answer it said shift the tip of graph four places right and one place up.

Any suggestions?

Fred Haynes
• Hmm I see your problem. In order to graph a function, you have to have it in vertex form;

a(x-d)² + c <---- Basic Form

Example: (x-3)² + 3
Since there's no a, you don't have to worry about flipping on the x axis and compressing or stretchign the function. Now we look at d. d = -3. In order to find the zeros of the function, x must equal 3. That's why the equation moves to the right when d is negative and when d is positive, the equation moves to the left. So simply to say, (x-d)² = 0 When you know d, then your x will be something that subtracts d to equal 0. So in this example, the function shifts 3 units to the right. Now we look at c. c is 3, which means that the graph moves 3 units up. And voila! There you have it! If you need more clarification, don't hesitate to ask. I hope this helped!
• If you are subtracting a number from x, wouldn't that shift it to the left since it would decrease the value of x?
• Think of the equations: g(x)=x and f(x)=x-1. The same value of g(x) and f(x) will be made by an x value one greater in the function f than the x from the function g . Therefore, the graph will move to the right.
• In the subsequent practice section, the term 'transformation' is used, not shift. I assume every shift is a transformation, but is every transformation a shift?
• No, other types of transformations are reflections, rotations, and dilations.
• Is it correct to say the function f(x) = x^2 can be shifted ONLY to the right e.g. g(x) = (x-2)^2, since the square of the calculation x-2 in parentheses will always result in a positive number?
Thanks.
• Think of the inside as shifting the '0' to the right or left. If you have x-2=0, x=2 so it shifts to the right. If you have x+2=0, you end up at x=-2 so it shifts to the left.
• at the time of 1.55, why we shift the coordinate (5,9) to the coordinate (5,5)?
• When comparing g(x) with f(x), we need to know not only what happens with the x values (shift 2 units to the right) but we also need to know what happens with the y values.
The constant term in f(x) is zero (in other words, there isn't one), but the constant term in g(x) is - 4. This tells us that the points in g(x) are 4 units lower than in f(x).
That's why (5,9) was moved down 4 units to reach (5,5).
Hope this helps!