SB 463 IGC – 2017-2018 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 inset 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 thetable 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 andhas a Range of [-1,6]. Write the correct equation for the line. Indicate the domain for thestreet.
7. Plot the location of the following public service buildings: Police station located at (-8,8), Fire stationlocated at (-10,2), and the Hospital located at (-2,11). Calculate the slope between the Police Stationand 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 forthe new street in slope-intercept form.
9. Create a u-turn street in your city modeled by a quadratic equation with the following conditions: avertex 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 aDomain of [-7, -1]. Place restroom facilities and a water fountain at the roots of the trail’s function. Placea 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.
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 rateof 5% per year. Answer the questions on your city key using this information.
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
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 = -.25x2 – x + 8
Please make sure that you show all your work and get these problems checked before you move on to the project
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)
