SPRING FINAL Review Algebra I 2016 1. (2C/3C) Write the equation of this line in standard form. 2.(5C) A system of equations is used to produce the set of points in the table below. What is the x value of the solution? 𝑥 −6 −3 𝑦 −18 −12 𝑦 18 12 4(2I) Write the equation of the line graphed below in slope-intercept form. 7. (6A) The table below shows ordered pairs that satisfy the quadratic function 𝑓. Between what 𝑥 𝑓(𝑥) interval would I find: −2 31 1. f(x) = 3 −1 20 0 11 2. f(x) = 0 1 4 2 −1 3. f(x) = -2.5 3 −4 4 −5 -4 5 3 0 0 6 -6 6 9 −12 12 3. (3B) What is the rate of change? 𝒙 5 4.5 2 1.5 0.5 y 60 180 240 540 600 5. (3C) The cost, 𝐶, of getting your car repaired is given by where ℎ is the number of hours in labor the mechanic works on your car, 55 is the cost per hour the mechanic charges, and 190 is the cost for the parts needed to repair your car. This situation is represented by 𝐶 = 55ℎ + 190. What would the 𝒚-intercept represent in this situation? 6. (5A) Solve the equation for 𝑥. 8. (8A) What are the zeroes of the function 𝑦 = 𝑥 2 − 16 9. (6A) What is the range of 𝑓(𝑥) = 2𝑥 2 + 9? 8(𝑥 − 6) = −2𝑥 − 6.9 SPRING FINAL Review Algebra I 2016 10. (7A) The table below represents a quadratic equation. Complete a new table and fill in the gaps as 𝑔(𝑥) 𝑥 best you can. 𝑥 −1 2 5 6 9 10 12 14 𝑔(𝑥) −55 −16 5 8 5 0 −16 −40 What are the zeros? 11. (6C) Write the quadratic equation of the graph below in vertex form. 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘 12. (7C) Write an equation for the function g(x) in vertex form. It is 𝑓(𝑥) = (𝑥 − 8)2 + 10 translated 2 units up and 5 units left. 13. (7B) A quadratic function 𝑓 has 𝑥-intercepts at −6 and 2. Write a quadratic function in standard form to represent this situation. What is the AOS? 14. (7A) Between what two numbers would I find the positive zero of this parabola? Between what two numbers would I find the negative solution? 15. (9C) The value of a boat is depreciating at a rate of 7% per year. In 2004, the boat was worth $192,000. Find the worth of the boat in 2013. 16. (9C) Suppose you deposit $500 in a savings account that pays .5% interest compounded monthly. Write an exponential function in the form 𝑦 = 𝑎𝑏 𝑥 that models the amount of money in your savings account for any month, x? How much would you have in 2 years? SPRING FINAL Review Algebra I 2016 17. (11B) Find the area of a square with a side length of: 18. (11B) Simplify the following expression: 1 6𝑥 7 𝑦 2 z−1 30𝑥 4 𝑦 2 𝑧 −4 (81𝑎6 𝑏 4 𝑐10 )2 inches. 19. (10E) The base of a right triangle is 4 inches less than twice its height. If the area of the triangle is 48 square inches, write an equation in standard form to find the height of the triangle in inches? 20. (7C) Given the following quadratic equations: 𝑓(𝑥) = −𝑥 2 + 64 𝑔(𝑥) = −2𝑥 2 − 51 ℎ(𝑥) = 𝑥 2 + 14 1. Do they have the same y-intercept? 2. Do they have the same axis of symmetry? 3. Do they have the same vertex? 4. Do they have a max or a min vertex? 1 22. (9D) The function 𝑓(𝑡) = 300(4)𝑡 represents the number of Moose in Yellowstone park after t years. If this function is graphed on a coordinate grid, what would be the meaning of the 𝑦 −intercept? 23. (10D) Simplify the following expression: 25. (7C) Identify the transformations of the graph of the parent function 𝑓(𝑥) = 𝑥 2 needed to obtain the graph of 𝑔(𝑥) = −3(𝑥 + 2)2 + 4. 26. (8A) What are the solutions to the quadratic equation: 𝑦 = 3𝑥 2 − 7𝑥 − 7 ? 24. (8A) What is the solution to: 5𝑥 2 − 14𝑥 = 3 (3𝑥 − 2)(5𝑥 + 7) 27. (10E) The area of a rectangular piece of wood is represented by: 2𝑟 2 − 13𝑟 + 21. Find the dimensions of the piece of wood.