Name: Date: Class Period: Algebra 2 Honors Semester 1 final Exam Review Part 2

Transcription

1 Name: Date: Class Period: Algebra 2 Honors Semester 1 final Exam Review Part 2 Outcome 1: Absolute Value Functions 1. ( ) Domain: Range: Intercepts: End Behavior: 2. ( ) Domain: Range: Intercepts: End Behavior:

2 Step Functions 3. ( ) Domain: Range: Intercepts: End Behavior: 4. ( ) Domain: Range: Intercepts: End Behavior:

3 Graph the piecewise function. 5. ( ) { Domain: Intercepts Range: End Behavior: Write a piecewise function for the graph below. 6. Domain: Range: Intercepts End Behavior::

4 Write and solve a system of equations for the following situation. 7. Sarah and Tony are selling loaves of bread for a school fundraiser. Customers can buy banana bread and pumpkin bread. Sarah sold 4 loaves of banana bread and 7 loaves of pumpkin bread for a total of $131.25, Tony sold 8 loaves of banana bread and 16 loaves of pumpkin bread for a total of $ What is the cost of each of one loaf of banana bread and one loaf of pumpkin bread? Solve each system using substitution or elimination

5 Solve each system by graphing Write a system of equations for each situation. Then, solve each system. 12. Billy s Restaurant ordered 200 flowers for Mother s Day. They ordered carnations at $1.50 each, roses at $5.75 each, and daisies at $2.60 each. They ordered mostly carnations, and 20 fewer roses than daisies. The total order came to $ How many of each type of flower was ordered?

6 13. Last Tuesday, Regal Cinemas sold a total of 8500 movie tickets. Proceeds totaled $64,600. Tickets can be bought in one of 3 ways: a matinee admission costs $5, student admission is $6 all day, and regular admissions are $8.50. How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets? Solve each matrix equation

7 16. A company manufactures and sells two models of lamps, L1 and L2. To manufacture each lamp, the manual work involved in model L1 is 20 minutes and for L2, 30 minutes. The mechanical (machine) work involved for L1 is 20 minutes and for L2, 10 minutes. The manual work available per month is 120 hours and the machine is limited to only 80 hours per month. Knowing that the profit per unit is $15 and $10 for L1 and L2, respectively, determine the quantities of each lamp that should be manufactured to obtain the maximum benefit. Define variables: Objective Function: Constraints: Vertices: How many L1 lamps and L2 lamps should be made in order to maximize profit? Is making 2 L1 lamps and 4 L2 lamps a viable production plan? Why or why not?

8 17. With the start of school approaching, a store is planning on having a sale on school materials. They have 600 notebooks, 500 folders and 400 pens in stock, and they plan on packing it in two different forms. In the first package, there will be 2 notebooks, 1 folder and 2 pens, and in the second one, 3 notebooks, 1 folder and 1 pen. The price of each package will be $6.50 and $7.00 respectively. How many packages should they put together of each type to obtain the maximum benefit? Define variables: Objective Function: Constraints: Vertices: How many of each type should be made to maximize the profit? Is making 150 of Package 1 and 50 of Package 2 viable production plan? Why or why not?

9 Outcome 2: 18. Find a quadratic model for the data. The table shows the average sale price p of a house in Suffolk County, Massachusetts, for various years t since a. Equation: b. Estimate when the average sale price will be thousand dollars. 19. Graph the function. Find the minimum or maximum value and the Axis of Symmetry. 20. What is the vertex of 21. The vertex of the function s graph is given. Find c. ( ) 22. Write the equation of each parabola in vertex form. Vertex ( ) ( ) 23. Write the function in vertex form. Identify the axis of symmetry. Describe the transformations.

10 24. For a model rocket, the altitude h, in meters, as a function of time t, in seconds, is given by. Find the maximum height of the rocket. How long does it take to reach the maximum height? Round to the nearest tenth. 25. Write the equation of a parabola that is reflected over the x-axis, has a horizontal expansion of a factor of 3 and is shifted to the left 9 and up Describe the transformation of the quadratic. ( ) 27. Write the verbal description for each graph. This means: describe how the parent function,, was changed to make the graph below. (There may be more than one thing changed.) Solve each system by graphing. 28. { ( ) 29. {

11 Determine the solution(s) to each system of equations. Round to the nearest hundredth. 30. { ( ) 31. { ( ) 32. x g(x) (Standard Form) ( ) (Vertex Form) ( ) (Vertex Form) ( ) Similarities Differences Describe the translations required to translate ( ) onto ( ): The y-coordinate of the y-intercept of ( ) The y-coordinate of the y-intercept of ( ) ( ) ( )

12 The distance the vertex is from the y-axis of ( ) The distance the vertex is from the y-axis of ( ) The distance the vertex is from the x-axis of ( ) The distance the vertex is from the x-axis of ( ) The axis of symmetry of ( ) The axis of symmetry of ( ) The min/max value of ( ) The min/max value of ( ) 33. An object in launched directly upward at 64 feet per second (ft/s) from a platform 120 feet high. a. What will be the object's maximum height? b. When will it attain this height? c. When will the object hit the ground? Round answer to the nearest hundredth if necessary. Solve each equation by factoring

13 36. The area in square centimeters of a square 37. Write a quadratic equation that has the given roots. mat is Find the dimensions (Write your final answer using only integers.) of the mat in terms of x. Simplify each expression completely. 38. ( )( ) 39. Simplify each expression completely. 40. ( )( )( ) 41. ( ) ( ) Solve each equation by using square roots

14 Solve each equation by completing the square Rewrite each equation in vertex form using completing the square. Then identify the vertex and y-intercept Determine the number of solutions and whether they are real or imaginary Solve each equation using the quadratic formula

15 52. After t seconds, a ball tossed in the air from the ground level reaches a height of h feet given by the equation. How long does it take for the ball to reach the ground again? Round your answer to the nearest hundredth. 53. A rocket carrying fireworks is launched from a hill 80 feet above a lake. The rocket will fall into lake after exploding at its maximum height. The rocket s height above the surface of the lake is given by. After how many seconds after it is launched will the rocket hit the lake? Round your answer to the nearest hundredth.