01. Solve linear equations in one unknown both algebraically and graphically.

Given:

A person cuts a rope into two pieces that are equal in length. The first piece is 4 times the length of the person’s forearm minus 1 inch. The second piece is 3 times the length of the person’s forearm plus 15 inches.

Task:

1. Construct the linear equation that represents the situation in the given using x as the variable for the person’s forearm.
2. Solve the linear equation you constructed both algebraically and graphically to find the length of the person’s forearm. Show your work.
3. Briefly discuss whether or not your answer is reasonable.

Note: To draw the graph, you may use one or a combination of the following:

- A spreadsheet program, such as Excel (*. xls )

- A graphics program, such as Paint (*.jpeg, *.gif)

- A word processing program, such as Word (*.rtf)

- A scanned hand-drawn sketch (*.jpeg, *.gif)

02. Solve quadratic equations in one unknown both algebraically and graphically.

Task:

1. Solve the following quadratic equations. Make sure to show all your work. Do not use any method (e.g., factoring, completing the square, quadratic formula, graphing) more than twice. Use the graphing method at least once .

1. 3 x 2 + 11 x – 20 = 0
2. x 2 + 3 x – 4 = 0
3. 3 x 2 – x – 1 = 0

B. State the different methods you used to solve each equation. Make sure that your work demonstrates both algebraic and graphing methods.

03: Explain why an answer to an algebraic or numerical calculation is unreasonable.

Task:

1. A school bus holds 57 students but is only 40% full. How many students are on the bus?

1. Explain why the answer of 22.8 students is unreasonable.
2. Give a reasonable answer in its place.
3. Explain why your answer is more reasonable.

B. The length of a rectangular field is 2 yards more than its width. Find the width if the area of the field is 120 yd 2 .

1. Explain why the answer of a width of –12 yards is unreasonable.
2. Give a reasonable answer in its place.
3. Explain why your answer is more reasonable.

04: Graph basic functions of one variable.

Task:

1. Graph the function f( x ) = –3 x + 7. Be sure to properly label the graph, which includes labeling the axes and the line with its equation.
2. Graph the function f( x ) = –3 x 2 + x – 5. Be sure to properly label the graph, which includes labeling the axes and the graph with its equation.

Note: To draw the graph, you may use one or a combination of the following:

- A spreadsheet program, such as Excel (*. xls )

- A graphics program, such as Paint (*.jpeg, *.gif)

- A word processing program, such as Word (*.rtf)

- A scanned hand-drawn sketch (*.jpeg, *.gif)

Price: $15.05

Solution: The downloadable solution consists of 8 pages, 705 words and 6 charts.
Deliverable: Word Document