Math 110                                                                                               Name:

Exam II: Chapter 3 and Exam I                                                            Date:  

 Directions: Show all work to get full credit.

Part I: Only scientific calculators allowed.

1. Simplify: 

2. Label each function as one of the following types: 

Linear, Quadratic, Absolute Value, or Square Root

3. Analyze the TABLE to find features of the parabola given by the function:  

x-intercept(s):                                        __________________

y-intercept:                                            __________________

vertex point:                                          __________________

axis-of-symmetry equation:                __________________

solution(s) to      __________________

4. Analyze the GRAPH generated by a quadratic function and give the following characteristics:

a.    The x-intercept(s)                                         _____________________

b.     The y-intercept                                            _____________________

c.        The vertex point                                           _____________________              

d.       The axis-of-symmetry equation                _____________________

e.        Domain                                                          _____________________

f.         Range                                                            _____________________

g.       Increasing interval                                     _____________________

h.       Decreasing interval                                    _____________________

i.         approximate Solution(s) to.      _____________________

5. Factor each expression completely. Remember to take out the GCF first (if it exists) and then factor:

a.        3x² + 5x – 2                                                                              b.    3x³ – 15x² + 12x

6. Situation:

A ladder is leaning up against the side of a house using the safe-ladder ratio 4 to 1. The side of the

house forms a 90 degree angle with the ground. The length of the ladder is 13 feet.

                 Question:

What is the distance from the base of the house to the base of the ladder (i.e. the distance along the

ground)? Round your answer to the nearest hundredths place.

7. Find the x-intercepts (i.e. zeros) of the function given using a symbolic method.

8. SOLVE the equations in parts ‘a’ – ‘d’. Use a symbolic method only (i.e. no tables or graphs).

Note: Solutions without showing work will receive no points. All numbers in your steps must be  

expressed in exact form (i.e. no decimal approximations).

a.   Use the quadratic formula method:                            

                 b.   Use the factoring method:                                          

                 c.   Use the completing the square method:    

             d.       

9. Fill-in-the-blanks:

1. The highest or lowest point on a parabola is called the _____________ point.

2. A ______________ is a letter representing a fixed value (such as g, v_o,h_o).

3. A parabola is the shape of a ________________ function.

4. The axis-of-symmetry line always passes through the ______________ point.

5. The degree of a function is the highest _______________ of all variables in the equation.

Part II:  Both scientific and graphing calculators are allowed.

10. Give all the information below about the graph of the basic square root function .

Domain:                                                                 ______________________________                 

Range:                                                                            ______________________________

x-intercept point(s):                                                     ______________________________

y-intercept point(s):                                                     ______________________________

where the function is increasing:                        _____________________________                    

where the function is decreasing:                       _______________________

11. Situation:  Imagine a diver (in Espanol: clavadista) diving off a cliff 40 feet high. The height of the diver at time t is given by the formula  where g is the acceleration due to gravity (32.2 ft/sec²). The diver’s initial velocity is 5 ft/sec.

             Questions:

·         What are the values of the parameters?

·         What do the variables represent?

·         What is the model equation for this situation?

·         How long does it take the diver to reach the water?

Parameter values

Variables 

                    t =

                    h =

                Model Equation

 How long does it take the diver to reach the water? Round to the nearest tenths place.