Exam 2 Review F15 O Brien. Exam 2 Review:

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1 Eam Review:.. Directions: Completely rework Eam and then work the following problems with your book notes and homework closed. You may have your graphing calculator and some blank paper. The idea is to practice working problems with no resources other than what you will have during the eam. This is will help you to identify your weak areas where you need further study. If you miss a problem practice working some problems like it with your book notes and homework open. Then work a few similar problems with your resources closed. Get in the habit of showing all of your support work on every problem.. Divide as indicated. Write the quotient in standard form...00 i i. Given P() = + do the following. Do not use a calculator... a. Write the function in the form P() a ( h) k + =. b. Give the verte of the parabola. c. Find four additional points and graph the function. +. Given f() = ( + ) do the following... a. Give the coordinates of the verte. b. Give the domain and range. c. Give the equation of the ais of symmetry. d. Give the largest open interval over which the function is increasing. e. Give the largest open interval over which the function is decreasing. f. State whether the verte is a maimum or minimum point and give the corresponding maimum or minimum value of the function.. Find the equation of the quadratic function having a verte of ( 6 ) passing through..8 the point (6 ). Epress your answer in the form P()= a + b + c.. A rock is launched upward from ground level with an initial velocity of 90 feet per second...6 a. Give the function s that describes the height of the rock as a function of t. b. How high will the rock be. seconds after it is launched? c. What is the maimum height attained by the rock? After how many seconds will this happen? d. After how many seconds will the rock hit the ground? 6. Solve the equation ( + ) = Solve the equation = 0 by completing the square...6

2 8. Solve each inequality analytically. Give eact values for endpoints...06 a b > 0 9. Solve V = π r h for r...0 Use algebra to solve the following applications. 0. ARC has plans to construct a rectangular parking lot on land bordered on one side by a.. highway. There are 60 feet of fencing available to fence the other three sides. What dimensions will give a maimum area and what will this area be?. A boat with a rope attached at water level is being pulled into a dock. When the boat is..7 feet from the dock the length of the rope is feet more than twice the height of the dock above the water. Find the height of the dock.. Suppose the revenue R in thousands of dollars that a company receives from producing.. thousand MP players is R() = (0 ). How many MP players should the company produce to maimize its revenue? What is the maimum revenue?. A frog leaps from a stump feet high and lands 6 feet from the base of the stump. The..8 height h in feet of the frog as a function of its horizontal distance from the base of the stump is given by h ( ) = + +. What was the horizontal distance from the base of the stump when the frog reached maimum height? What was the maimum height?. Use your graphing calculator to find a comprehensive graph of the function..6 P() = and then answer the following questions. Round all approimate values to the nearest hundredth. a. Predict the end behavior before you graph the function. b. Find all local minimum points and tell if any is an absolute minimum point. c. Find all local maimum points and tell if any is an absolute maimum point. d. Give the domain and the range. e. Find all intercepts. f. Give the open intervals over which the function is increasing. g. Give the open intervals over which the function is decreasing.. Use long division to find the quotient when P() = is divided by Use synthetic division to find P(k) when k = and P( ) + = Use synthetic division to determine if is a zero of P( ) =..6.7

3 8. is one zero of the polynomial P() = Find all the other zeros of P.6.70 analytically. Give your answers in eact form. Do not use a calculator. 9. Factor P() = 6 + into linear factors given that is a zero of P Divide Find a cubic polynomial in standard form with real coefficients having zeros of.7. and 6 + i. Let the leading coefficient be. Do not use a calculator.. is a zero of the polynomial P() = + 7. Find all remaining zeros..7.. Use the graph below to write an equation for f() in factored form. Assume that all.7. intercepts have integer coordinates and that f() is either a cubic or quartic polynomial.. Given P() = a. List all possible rational zeros. b. Use a graph to eliminate some of the possible rational zeros listed in part a c. Find all zeros. d. Factor P() into linear factors.. Solve each equation analytically giving eact forms of your solutions. a. + 8 = ( + 7) [.8.] b. 9 + = 0 [.8.0] c. + = 0 [.8.] d = 0 [.8.8] 6. Do.8 #77 p. 9

4 7. Eplain how the graph of f() = can be obtained from the graph of y =. +.. Draw a sketch of the graph of by hand. And give the domain and range of f(). 8. Use the method described in Eample on page 7 to rewrite Then sketch the graph of f() by hand. f() = Give the equations of any vertical or horizontal asymptotes for the graph of.. f() = and state the domain of f Sketch the graph of and intercepts. f() =. Your graph should include all asymptotes holes Find all comple solutions for each equation by hand. Do not use a calculator. a. = 0 [..6] b. + = [..6]. Determine the domain of f ( ) + =. Do not use a calculator...7. Given f() = use a graph to find the following...8 a. the range; b. the largest open interval over which the function is increasing; c. the largest open interval over which the function is decreasing; d. the solution to the equation f() = 0.. Solve the equation 8 = by hand. Do not use a calculator.... Solve the equation + = by hand. Do not use a calculator...

5 Answers. i. a. P( ) 7 7 = + b. c. y a. ( ) b. D: ( ) R: ( ] d. ( - ) e. ( ). P( ) = + f. Maimum; c. = a. s(t) = 6t +90t b. 99 ft c. 6.6 feet;.8 sec d..6 secs 6. + i i 7. ± 6 or ± 6 0 8a. 0 b. ( ) 9. ± r = Vπ h π h ft by 0 ft; 00 ft. ft. 0000; $ ft;. ft. a. LH RH b. (.6.69) is an absolute min; ( ) D : ; R : [.69 ) No. c. (.7 7.8) is not an absolute ma d. ( ) e. -intercepts: ( 0) ( 0); y-intercept: (0 7) f. (.6.7); (.68 ) g. (.6); (.7.68) P() = 6 + or P() = ( + ) ( + ) ( ) 9. ( ) P( ) =

6 . + i i. f() = ( + ) ( + ) ( ) ( ). a. ± p q = ± a. 6. b. Eliminate values less than or greater than c. d. P() = ( + ) + or P()=( + ) ( + ) ( ) ± b. {..} c. {. 0 } d. { ± 9} 7. To obtain the graph of f() = + vertically stretch the graph of y = by a factor of. Shift it to the left and down. Domain: ( ) ( ) Range: ( ) ( ) 6

7 8. f ( ) = VA: = ; HA: y = ; Domain: 0. VA: = ; HA: y = ; hole: ( ) -intercept: ( 0); y-intercept: (0 ). a. {} b. Ø. D:. a. [ 0 ) b. ( ) c. none d. { }. { }. { 0} 7