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Learning Math Home
Patterns, Functions, and Algebra
 
Session 6 Part A Part B Part C Part D Homework
 
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Session 6, Part D:
Solving Systems of Equations

In This Part: Solving balance Equations by Graphing | Non-Linear Graphs

The next graph requires seven counters. Follow these instructions:

a. 

Line up the counters along the x-axis at each integer value between and including -3 and +3.

b. 

At each point, multiply the x value by itself. Move the counter vertically to the result.


 

Problem D8

Solution  

What is the shape of this graph? Where is the "lowest" point? Can you explain why this is the lowest point of the graph?
Note 12


Take it Further

For the next graph, follow these instructions:

a. 

Place counters along the x-axis at each integer value between and including -3 and +3.

 

b. 

At each point, multiply the x value by itself, then subtract 2 from the result. Move the counter vertically to the result.


Problem D9

Solution  

On this graph, can you identify the x-intercepts of the graph? Can you identify the "lowest" point on the graph?

 

See the definition of an (link to the pop-up window?)x-intercept   Close Tip

 

Problem D10

Solution  

Use counters to find all intersections of the graphs of y = x2 - 2 and y = x.

 
 
  

A system of equations is any situation where more than one equation results. Try to solve this system of equations any way you can:

 
 

Problem D11

Solution  

Joe buys coffee and donuts for the office each week. The local donut shop always charges the same amount for each cup of coffee and for each donut. One week, Joe bought 12 donuts and 6 cups of coffee, and the total was $15.00. The next week, Joe bought 7 donuts and 6 cups of coffee, and the total was $11.50. Use this information to figure out how much each cup of coffee and each donut costs.

 

What did each of Joe's trips have in common? What changed? How does this change help you find the price of each item?   Close Tip

 

Next > Homework: Balance Puzzles

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