Vertical Translations of Graphs

Discover and Explore Vertical Translations of Graphs

Scope and Sequence

Ninth Grade: Integrated
Patterns and Relationships #4: Use a graphing calculator or computer to generate the graph of a function.
Tenth Grade: Integrated
Algebra #5: Symbolize transformations of figures and graphs.
Algebra #7: Graph linear functions.
Eleventh Grade: Integrated
Patterns and Relationships #3: Use a graphing calculator or computer to graph functions.

Find a website that can graph equations. Use this site to explore vertical translations.

1.) Graph the following equations:
a.) y = x
b.) y = x + 2
c.) y = x - 3

Equations like the ones above are called linear equations. This is because they all resemble lines. The equation that you graphed in part a is called the parent graph to all linear equations. This is because all linear equations are derived from the parent graph. We start with y = x and then by adding / subtracting / multiplying / dividing, we can obtain any other linear equation that we wish.

2.) Look carefully at the graphs that you obtained in part 1 above. Write at least 5 sentences comparing and contrasting these three graphs to each other. I want you to compare b to a, and c to a. Remember that a is the parent graph. Tell me what happened to the graph when you added or subtracted to or from x.

3.) Now that you have done that I want you to tell me in words, without graphing, what do you think the following graphs will look like as compared to the parent graph.

a.) y = x + 3
b.) y = x - 6
c.) y = x + 7
d.) y = x - 5
e.) y = x + 25
f.) y = x - 30

4.) Now graph the following equations:

a.) y = x^(2)
b.) y = [x^(2)] + 3
c.) y = [x^(2)] - 4

Equations such as the ones in part 4 are called quadratic equations. The highest degree variable in a quadratic equation is second degree, or squared. They all resemble the same shape. This shape is called a parabola. The equation that you graphed in part a is called the parent graph to all parabolas or second degree equations. This is because all quadratic equations are derived from the parent graph. We start with y = x^(2) and then by adding / subtracting / multiplying / dividing, we can obtain any other parabola that we wish.

5.) Now look carefully at the graphs that you obtained in part 4 above. Write at least 5 sentences comparing and contrasting these three graphs to each other. I want you to compare b to a, and c to a. Remember that a is the parent graph. Tell me what happened to the graph when you added or subtracted to or from x.

6.) Now that you have done that I want you to tell me in words, without graphing, what do you think the following graphs will look like as compared to the parent graph.

a.) y = [x^(2)]+ 6
b.) y = [x^(2)]- 12
c.) y = [x^(2)]+ 8
d.) y = [x^(2)]- 5
e.) y = [x^(2)]+ 9
f.) y = [x^(2)]- 1

7.) Fill in the blanks.

Linear equations are also called _____________degree equations. This is because all the variables are in the __________ degree.
When you add a constant (another word for a number without a variable) to a variable in a first degree equation or second degree equation, it causes the whole graph to shift _______ the number of units of the constant. When you subtract a constant from a variable in a first degree or second degree equation, it causes the whole graph to shift ____________ the number of units of the constant. This is why it is called vertical shifting, because vertical represents the _________ and ___________ direction.

8.) If I told you that y = x^(3) was the parent graph for cubic or third degree equations, what do you think would happen to the graphs of y = [x^(3)] + 5 and y = [x^(3)] - 18 ? Answer with a minimum of 5 sentences.

In order to get full - credit for this assignment make sure that you followed all the above directions.