Algebra for All Year 2

Algebra For All year 2 Capstone Project Lisa Jacobs, Truman High School, Taylor

Shapes of Algebra ! Transformations overview

This activity is intended for an Algebra 1 class , near the end of the year , after covering linear, quadratic, and exponential functions.

Part 1: Transformations overview Three different groups will each explore one of the function families, and make a large poster graph of the 5 functions in that family, one being the parent function.

Before doing Part 2, have the groups explain their graphs, what they can see at that point in patterns, what the parent function is and looks like. Either have students write each table of values on the poster or use a document camera to show the tables of values. Then possibly have groups of students do a gallery walk around to view each exploration closely to answer the Part 2 questions.

Part 3 : Individually, have students match the symbolic rules given with the appropriate graph, using the patterns discovered in the previous parts.

Part 4 Is it Linear, Quadratic, or Exponential ? Students can identify which family of function each real situation represents.

Part 5 Table time for Families. Identify which family of functions is represented by each table of values.

Discussion of these results (how each family have common characteristics, how the “offspring” are different from the parents) and then possibly a quiz can follow this activity. Exploration #1 Shapes of Algebra ! Name______Transformations overview Date______Hour______Group members: Part 1 Your group will : 1. For each rule in the set, produce a table of ( x, y ) values with integer values of x .

2. Draw the Graph for each of the symbolic rules with the table of values that you made. (Hint: don’t forget to draw the x & y axes…and put each table ON the large post-It graph paper) Draw the parent function with black , and use a different color for other graphs, as indicated.

3. Label each graph with it’s equation. Include a title.

Work area for table of values

a) y  x Parent Function for the ______Family. X -3 -2 -1 0 1 2 3 black Y

b) y  x X -3 -2 -1 0 1 2 3 Y red

c) y  2x X -3 -2 -1 0 1 2 3 Y purple

d) y  (x  4) X -3 -2 -1 0 1 2 3 Y green

e.) X -6 -5 -4 -3 -2 -1 0 Y blue USE THESE TABLES OF VALUES TO MAKE ORDERED PAIRS (X, Y) THEN PLOT THESE POINTS FOR EACH GRAPH.

Exploration #2 Shapes of Algebra ! Name______Transformations overview Date______Hour______Group members: Part 1 Your group will : 1. For each rule in the set, produce a table of ( x, y ) values with integer values of x .

Work area for table of values a) y = x 2 Parent Function for the ______Family. X -3 -2 -1 0 1 2 3 black Y b) y  x 2 X -3 -2 -1 0 1 2 3 Y red

c) y  2x2 X -3 -2 -1 0 1 2 3 Y purple

2 d) y  x  4 X -3 -2 -1 0 1 2 3 Y green

e.) y = ( x + 3 )2 X -6 -5 -4 -3 -2 -1 0 Y blue USE THESE TABLES OF VALUES TO MAKE ORDERED PAIRS (X, Y) THEN PLOT THESE POINTS FOR EACH GRAPH.

Exploration #3 Shapes of Algebra ! Name______Transformations overview Date______Hour______Group members: Part 1 Your group will : 1. For each rule in the set, produce a table of ( x, y ) values with integer values of x .

Work area for table of values

a) y  2x Parent Function for the ______Family. X -3 -2 -1 0 1 2 3 Y black

b) y  2x X -3 -2 -1 0 1 2 3 Y red

x c) y  (2)2 X -3 -2 -1 0 1 2 3 Y purple

x d) y  2  4 X -3 -2 -1 0 1 2 3 Y green

e.) y = 2x+3 X -6 -5 -4 -3 -2 -1 0 Y blue USE THESE TABLES OF VALUES TO MAKE ORDERED PAIRS (X, Y) THEN PLOT THESE POINTS FOR EACH GRAPH.

Part 2 Shapes of Algebra ! Observations of graphs / description of patterns of transformations Objectives: Compare the tables, graphs, and symbolic rules in the explorations. Note similarities, differences, and connections between the symbolic rules and the table and graph patterns.

Answer the questions using the graphs &/or tables of all the explorations.

1. In “a” of each exploration, state the rule for the parent function , and describe it’s graph.

i. Exploration 1: rule______graph______ii. Exploration 2: rule______graph______iii. Exploration 3: rule______graph______

2. In “b” of each exploration, identify what the “ – “ sign does for each exploration’s graph.

iv. Exploration 1: ______v. Exploration 2: ______vi. Exploration 3: ______vii. Generalizing, how does the “ – “ sign affect graphs?

3. In “ c” of each exploration, how does the coefficient a change the graphs ?

viii. Exploration 1: ______ix. Exploration 2: ______x. Exploration 3: ______

3. In “d”of each exploration, how does subtracting 4 from the parent function change the graphs?

xi. Exploration 1: ______xii. Exploration 2: ______xiii. Exploration 3: ______xiv. Generalizing, how does subtracting at the end of a function affect(move) the graph?

xv. How do you think adding a value at the end of a function affects/moves a graph?

4. In “e” of each exploration, how does adding 3 directly to x affect the graphs ?

xvi. Exploration 1: ______xvii. Exploration 2: ______xviii. Exploration 3: ______xix. Generalizing, how does adding a value directly to x affect( how does the graph move) each graph? xx. How do you think subtracting directly to x would affect each graph? Part 3 Shapes of Algebra ! Use the information from parts 1 & 2 to help match the following graphs with the symbolic rules(equations).

Equation:______Equation:______Equation:______

Part 4 Shapes of Algebra ! Is it Linear, Quadratic, or Exponential ?

State whether the following situations would be best represented by a linear, quadratic, or exponential graph.

1. Mr. Bee’s free throw shooting ( the flight of the ball ).______

2. Population growth of the number of snails in an aquarium.______

3. The flight of an arrow that is shot in the air on an upward angle.______

4. The path of an airplane descending from 20,000 to 10,000 feet.______

5. The amount of water in an aquarium when filling up.______

6. The total amount of money spent on prom tickets in relation to the number of people going.______

7. The amount of money in a savings account that uses compound interest.______

8. The flight of a dolphin jumping out of the water at Sea World.______

9. The population of pandas if the population is half of each previous year.______

10. The flight of a tee shot by Tiger Woods.______

11. The number of miles driven on a freeway when traveling at a constant speed.______

12. The value of a used Honda Accord over time.______

13. The height of a flea that jumps onto a cat. ______

Part 5 Table time for Families. Identify which family of functions is represented by each table of values. What are you looking for to identify the correct family it belongs to ?

Table A Table B Table C x -2 -1 0 1 2 y -7 -5 -3 -1 1

Family______Family______Family______