SB 463 IGC ALGEBRA I Adapted from Houston ISD Curriculum

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1 SB 463 IGC ALGEBRA I Adapted from Houston ISD Curriculum EOC Project: Create Your Own City Map As a city planner, you have been asked to create a street-map and master plan for a new sub-division that is being developed. Your final product must be represented on a coordinate plane and include all of the guidelines and requirements listed below. Project guidelines: All streets must be labeled with the name of the road. Buildings and landmarks must be labeled. Lines cannot be horizontal or vertical unless otherwise denoted. Each of the following community requirements must be represented by a different equation. For instance, you may not use the same equation to satisfy two different requirements. The map should be easy to read and colorful be creative! Community Requirements: 1. Locate and plot the City Central Square at the origin. 2. Draw a street that models the parent linear function and place your house at point (3,3). 3. Create one street modeled by a line with a positive slope passing through the points (-8,0) and (0,6). Write the correct equation for the line in function notation. Indicate the Domain and Range in set notation for the street. 4. Create one street modeled by a line with a negative slope passing through the points (0,-2), and (-7,0). Write the correct equation for the line in standard notation. Create a billboard that shows the table that corresponds to this linear equation (contains at least 4 points). 5. Create one street modeled by a line with a slope of 0 and has a y-intercept of -12 and a Domain of (-,10]. Write the correct equation for the line. Indicate the range for the street. 6. Create one street modeled by a line with an undefined slope that intersects your house and has a Range of [-1,6]. Write the correct equation for the line. Indicate the domain for the street. 7. Plot the location of the following public service buildings: Police station located at (-8,8), Fire station located at (-10,2), and the Hospital located at (-2,11). Calculate the slope between the Police Station and Hospital using only the slope formula. 8. Create a street that is parallel to the line from #4 that has a y-intercept of -6. Write the equation for the new street in slope-intercept form. 9. Create a u-turn street in your city modeled by a quadratic equation with the following conditions: a vertex at (3,6), a y-intercept of 10.5 and an a value of!. Write the function that models this u-turn in! vertex form and find the Line of Symmetry. 10. Create a park in your city by shading the region bounded by the equations from #2, #3, #4 and #8. Using the equations for those lines, correctly determine the inequalities that define the shaded region. 11. Create a hike and bike trail that models the following quadratic function: y = 2x! -16x -23 with a Domain of [-7, -1]. Place restroom facilities and a water fountain at the roots of the trail s function. Place a bench at the vertex of the trail s function. 12. Plot points to represent ten different businesses with a negative correlation in Quadrant IV. 13. Use substitution to find the intersection of the lines from #2 and #4. Page 1 of 3

2 14. Find the Exponential equation that passes through the following points: (-1,!! ), (0,1), (1,2), (2,4), (3,5). Indicate the Domain and Range in set notation for the street. 15. The population of your city in 1990 was 400,000 and is growing at a rate of 5% per year. Answer the questions on your city key using this information. Page 2 of 3

3 Vocabulary (Define and give example/picture) 1. Domain: 2. Range: 3. Vertex: 4. Origin: 5. Correlations: 6. Function Notation: 7. Parallel Lines: 8. Root: 9. Slope: 10. Y Intercept: 11. Intersection: 12. X-Intercept: 13. Zero: 14. Coordinate: 15. Axis of Symmetry: 16. Exponential Function: Examples Student Guided Practice/Supplemental Aid A. Write a linear equation that crosses the points (0,0) and (15,15) B. Create a table using the following equation y = -3x + 8 C. Find the equation that is parallel to y = 12x - 2 and crosses the point (6,2) D. Graph the following inequalities y 17x + 3 and y < -6x -2 E. Find the solution to the systems y = 4x 2 and y = -.5x +8 F. Graph, find the roots, vertex and the line of symmetry of y = -.25x 2 x + 8 Please make sure that you show all your work and get these problems checked before you move on to the project Page 3 of 3

4 City Key Use the following template to record the required information for your city map. 1 Write the coordinates for City Central Square: 2 Write the name of the street in which your house is located on: Write the linear parent equation where your house is on: 3 Write the name of the street that has a positive slope and goes through points (-8,0) and (0,6): Write the equation for the line in function notation: Identify the domain, in set notation, of the street: Identify the range in set notation of the street: Is your street parallel to this new street? (Explain) Page 4 of 3

5 4 Write the name of the street that models a line with a negative slope and crosses the points (-7,0) and (0,-2): Write the equation of the line in standard notation (show your work): Create a billboard that shows the table that corresponds to this linear equation. Show your work by using substitution. x y Explain the difference between a positive and negative slope lines (Write in complete sentences) Which street is steeper between question 3 and question 4? 5 Write the name of the street that has a slope of zero which has the y- intercept of -12 and domain is (-, 10]: Write the equation of that line: State the range of this street in inequalities format: Page 5 of 3

6 6 Write the name of the street that has an undefined slope that intersects with your house: Write the function of that street: What is the domain when the range is [-1,6]? What is the difference between the domain an range on this street? 7 Find the slope between the hospital and police station (Use the slope formula only) 8 Create a street that is parallel to the street on question #4 and has the y-intercept at -6. What is the name of that street: What is the equation of that parallel street? Explain why these two streets are parallel by using complete sentences: Page 6 of 3

7 9 What is the name of the U-turn street: What is the equation of this street? (in vertex form) What is the equation of the line of symmetry: Explain the transformation from the parent quadratic function and this street: Page 7 of 3

8 10 What is the name of the park: Write the four inequalities that you used to make the park: 11 What is the name of the quadratic trail represented by y = -2x 2-16x + 23? What is the location of the bench? (use the axis of symmetry) What is the location of the restrooms and water fountains? (use the quadratic formula): Page 8 of 3

9 12 List all the coordinates that represent the businesses: Business 1: Business 2: Business 3: Business 4: Business 5: Business 6: Business 7: Business 8: Business 9: Business 10: Explain why the coordinates have a negative correlation: 13 Where do the streets intersect? use substitution method to prove it) Page 9 of 3

10 14 What is the exponential equation of the street? (show your work) What is the domain of this street? (use set notation) What is the range of this street? (use set notation) 15 What will the current population be? Using your calculator, determine in what year will the population reach one million: Page 10 of 3

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12 EOC Project: Create Your Own City Map - Rubric Alignment Project Requirements Scoring* Guided Notes / Supplemental Aids Checkpoint Community Requirement A.3(C) Community Requirement A.2(A) Community Requirement A.2(C) Community Requirement A.2(A) Community Requirement Checkpoint Community Requirement A.3(B), A.3(A) Community Requirement A.2(B) Community Requirement A.6(B), A.7(C), A.8(A) Community Requirement A.2(H), A.3(H), A.C(D) Community Requirement Checkpoint A.7(A), A.6(A), A.6(B) Community Requirement Community Requirement A.3(F), A.5(C) Community Requirement A.9(E), A.9(C), A.9(A), A.9(D) Community Requirement A.9(E), A.9(C), A.9(A), A.9(D) Community Requirement Checkpoint City Map Key Follows guidelines Demonstrates accurate mathematical understanding Professional Representation Demonstrates sufficient progress on project development Demonstrates high standards for quality and neatness Produces creative and innovative map Correlates work to the map OVERALL SCORE (>69 is the passing standard) * Shows complete understanding of the required mathematical knowledge. The solution completely address all mathematical components presented in the task. Shows nearly complete understanding of required mathematical knowledge. The solution addresses almost all mathematical components presented in the task. There may be minor errors. Shows some understanding of required mathematical knowledge. The solution addresses some, but not all mathematical components presented in the task. Shows limited or no understanding of the problem, perhaps only recopying the given data. The solution addresses none of the mathematical components required to solve the task.