Fall Final Exam Review 2012		Algebra 2		Name _________________________
									Period  _____
1.  Name the parent graph and describe the transformations:
a.             		b.             		c.  

2.  Let be the transformation of down 3 and left 5 of . 
 Write the rule for . 	_________________________________________		

3.  Reflect the graph of  across the x-axis, and vertically dilate by a factor of 2.			
__________________________________________

4.   Use the description to write the quadratic function in vertex form.  The parent function  is vertically compressed by a factor of  and then translated 2 units right and 1 unit down to create  _______________________.

5.  Given the function: .

     Does it open up or down?       Axis of symmetry ________  Vertex ________   Y-intercept _______

6.  Find the following for the function:  
  
      Is the vertex a Max or Min?   What is its value? _______  

    	Domain ____________       Range_____________

7.   Graph the function.  Identify the vertex and four 
      additional points.  Identify the equation of the axis of 
      symmetry.   

8.  Write the equation for the graph shown.

Find the zeros of each function by any method.
9.                                      			10.  

Find the roots of each equation using factoring.
11. a)                                   			12. a) 

b)     				     	     	      b) 

13.  Write a quadratic function in standard form with zeros  and .

14.  A rocket is launched from ground level with an initial velocity of 480 ft/s.  After how many seconds     will the rocket hit the ground?  Use  .

Solve each equation by using the quadratic formula.
15.                                      				16.     

Write each function in vertex form and identify its vertex , axis of symmetry, and the y-intercept.
17.                              			18.     

Vertex = _________						Vertex = _________
Axis of symmetry =__________				Axis of symmetry =__________
y-intercept = ________					y-intercept = _______

19.  Rewrite in standard form.  Identify the leading coefficient, degree of the polynomial, and the number of terms. 
	
	  polynomial			standard form		leading	degree	        number
							         			coefficient		       of terms
a).  	       	__________________________	_____		_____	          _____  
      
b).  __________________________	_____		_____            _____

20.  Add or subtract.  Write your answer in standard form. 
	a).          	  		   b).      

21.  Find each product.  
	
      	a.)       		b.              	c.)  

22.  Divide by using long division 
a.) 					b.) 

23.  Divide by using synthetic division.  
a.) 					b.)  

24.  Use synthetic substitution to evaluate the polynomial for the given value.    .
      for 							P(4) = ________

25.  Express  in terms of i.  

26.  Find the complex conjugate of each of the following.       A)             	B)  

Questions 27-29
For each quadratic equation , 	A)  find the value of the discriminant 
B)	find the type and number of solutions for each equation
C)	find the complex solutions  

27.  	A) ________		B)__________________	C) ____________________

28.  	A) ________		B)__________________	C) ____________________

29.   	A) ________		B)__________________	C) ____________________

30.  What is the solution of ?

31.  What is the solution of  ?

32. Write a quadratic inequality for this graph.

33.  Write a quadratic inequality for this graph.

Perform the indicated operation and write each answer in form.  

34.  					35.  
36.  						37.  

38.   Adeline hits a volleyball with an initial vertical velocity of 20 ft/s from a height of 4 feet .  Write a function h in standard form for the ball’s height in feet in terms of the time t in seconds after the ball is hit.  Then find the maximum height of the ball and the number of seconds (to the nearest hundredth) for the ball to hit the ground.
 
Function ______________________	  maximum height = _________   seconds to hit the ground _______

Find the zeros of each function by factoring.

39.  a. 			40. a.  		41. a.  

      b.  		      b.  		     b.   

42. Suppose a quadratic function contains the point  and has an axis of symmetry of x = 6.   
      Name one other point that would have to be on the graph of the function. 
					Second point that must be on the graph	______________

43.  Solve the equation 

44.  Explain how to find the y-intercept of any function.
 
45.  Suppose the leading coefficient of a quadratic function is a positive number and  
       the vertex is at the point . What is the range of the function?

46.  If   were moved up 4 and right 12, what is the equation of the new function?

47. Which method would be the best choice for solving the system given?

48. Which method would be the best choice for solving the system given?

  
 49.  Solve the system of equations using the method of your choice. 

50.	Solve the system of equations using the method of your choice. 

51. Classify each of the graphs of the polynomial functions below by their degree and leading coefficient.  Then determine the end behavior of each graph.
a. 				b.			   c. 				d.

Circle the correct choice.
Degree: Even or Odd		Degree: Even or Odd	       Degree: Even or Odd	      Degree: Even or Odd	

Leading Coefficient is		Leading Coefficient is       Leading Coefficient is	      Leading Coefficient is
Positive or Negative		Positive or Negative	       Positive or Negative	      Positive or Negative

52. Fayetteville Country Club golf course charges $10 to rent golf clubs plus $30 per 
       hour for golf cart rental.  Springdale Country Club golf course charges $15 to rent 
       clubs plus $25 per hour to rent a cart.  

a)	Write an system of linear equations to find the number of hours 
for which the rental cost is the same.

      b)  Graph the system.

      c)  For what number of hours is the cost of 
           renting clubs and cart the same for each course?  

      d)  How much would it cost for that number of hours?

53.Graph the system of inequalities:  		

54. Use your graphing calculator to estimate the real zeros, local maximum, and local minimum of 
.  Round your answers to the nearest thousandth.

a. real zeros __________, __________, _________    b. maximum _______ c. minimum _______

55.   Solve by finding all roots by using the calculator to find as many rational roots as possible, then use synthetic division and the quadratic formula to find the remaining roots.  Show all work!