MAT 1033C -- Martin-Gay Intermediate Algebra Chapter 8 (8.1, 8.2, 8.5, 8.6) Practice for the Exam

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1 MAT 33C -- Martin-Ga Intermediate Algebra Chapter 8 ( ) Practice for the Eam Name Date Da/Time: SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Fill in the blank with one of the words or phrases listed below. quadratic formula quadratic discriminant ± b completing the square quadratic inequalit (h k) (0 k) (h 0) -b a 1) The helps us find the number and tpe of solutions of a quadratic equation. 1) ) If a = b then a =. ) 3) The graph of f() = a + b + c where a is not 0 is a parabola whose verte has -value of. 3) 4) A(n) is an inequalit that can be written so that one side is a quadratic epression and the other side is 0. 4) ) The process of writing a quadratic equation so that one side is a perfect square trinomial is called. ) 6) The graph of + k has verte. 6) 7) The graph of ( - h) has verte. 7) 8) The graph of ( - h) + k has verte. 8) 9) The formula = -b ± b - 4ac a is called the. 9) ) A equation is one that can be written in the form a + b + c = 0 where a b and c are real numbers and a is not 0. ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use the square root propert to solve the equation. 11) = 11 A) B) 60. C)11 D) ) 1

2 1) = 1 A) 1 B) 1 C) D) ) 13) = 96 13) A) B) 48 C)4 6 D) 16 14) ( + 8) = 0 14) A) B) C) - D) ) = 0 1) A) B) -i 1 i 1 C) -1i 1i D) ) ( + 3) = 16) A) B) - 8 C) D) Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. 17) A) = ( + 9) B) = ( + 3) C) = ( + 36) D) = ( + 6) 17) 18) A) (-64) = ( - 8) B) = ( - 8) C) (-6) = ( - 16) D) = ( - 16) 18) 19) ) A) = C) = - 11 B) = D) =

3 0) ) A) = + 13 C) = B) = D) = Solve the equation b completing the square. 1) = 0 1) A) 3-1 B) 36 4 C) - -4 D) 4 ) = 0 ) A) B) C) D) ) = 0 3) A) -3-9 B) i -6-3i C) i D) -6-9i i 4) + 13 = -1 4) A) B) C) D) ) = 0 A) - i 7 + i C) - - i 7 + i B) - i i D) - - i i ) Use the quadratic formula to solve the equation. 6) = 0 6) A) -1-8 B) 1-8 C) -1 8 D) ) = 0 7) A) -8 B) -8 - i -8 + i C) -8 8 D) 8 8) = 0 8) A) B) C) D)

4 9) + 8 = - 1 9) A) B) C) D) ) = 0 A) -9 - i i B) ) C) 9 - i i D) ) z - = z ) A) 3 4 B) C) D) ) ( + 3)( - 1) = 4 3) A) B) 1 - i i 3 C) -1 - i i 3 D) ) ( + 8)( - 9) = ( - 1) - 7 A) B) ) C) 1 D) Use the quadratic formula and a calculator to approimate the solution to the nearest tenth. 34) = 0 34) A) = 6 = -7.3 B) = 1.7 = -0.4 C) = 0.8 = -3.4 D) = 0.4 = -1.7 Solve. 3) A ball is thrown upward with an initial velocit of 4 meters per second from a cliff that is 30 meters high. The height of the ball is given b the quadratic equation h = -4.9t + 4t + 90 where h is in meters and t is the time in seconds since the ball was thrown. Find the time that the ball will be 60 meters from the ground. Round our answer to the nearest tenth of a second. 3) A).3 seconds B) 9.3 seconds C) 9. seconds D).4 seconds 36) The revenue for a small compan is given b the quadratic function r(t) = 8t + 6t where t is the number of ears since 1998 and r(t) is in thousands of dollars. If this trend continues find the ear after 1998 in which the compan's revenue will be $930 thousand. Round to the nearest whole ear. 36) A) 003 B) 00 C) 004 D) 001 4

5 Use the discriminant to determine the number and tpe of solutions of the equation. 37) = 0 A) two comple but not real solutions B) two real solutions C) one real solution 37) 38) - 3 = 3 + A) one real solution B) two real solutions C) two comple but not real solutions 38) 39) = 0 A) two comple but not real solutions B) two real solutions C) one real solution 39) 40) 4 = 3-3 A) two comple but not real solutions B) two real solutions C) one real solution 40) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Sketch the graph of the quadratic function. Give the verte and ais of smmetr. 41) f() = )

6 4) f() = ( - 4) 4) ) f() = ( + ) ) ) f() = 44)

7 4) f() = 1 3 ( + 4) + 1 4) ) f() = 4( - 4) ) ) f() = -( + ) 47) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the function in the form = a( - h) + k. 48) f() = A) = -( - ) - 80 B) = -( + ) - C) = -( + ) + 0 D) = -( - ) ) 7

8 49) f() = A) = ( - 7) + B) = ( + 7) C) = ( - 14) + 39 D) = ( + 7) ) Find the verte of the graph of the quadratic function. 0) f() = A) (3 6) B) (-3-1) C)(6-3) D) (-3-30) 0) 1) f() = A) ( 19) B) (-1 6) C)(- 61) D) (1 -) 1) ) f() = A) (-8 11) B) (4-3) C)(4 -) D) (-4 41) ) 3) f() = A) (-9 17) B) C) D) (11 -) 3) Solve. 4) Find two numbers whose sum is 118 and whose product is as large as possible. [Hint: Let and be the two numbers.their product can be described b the function f() = (118 - ).] A) 1 13 and B) 8 and 60 C)9 and 9 D) 9 and ) ) An arrow is fired into the air with an initial velocit of 64 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given b the function h(t) = -16t + 64t. Find the maimum height of the arrow. A) 64 ft B) 3 ft C)96 ft D) 19 ft ) 6) The length and width of a rectangle must have a sum of 34 feet. Find the dimensions of the rectangle whose area is as large as possible. A) length 1 13 ft; width ft B) length 16 ft; width 18 ft ) C)length 17 ft; width 17 ft D) length 17 ft; width 1 ft 7) The cost in millions of dollars for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize the cost. A) 1 thousand automobiles B) 1 thousand automobiles C) thousand automobiles D) thousand automobiles 7) 8

9 Find the maimum or minimum value of the function. Approimate to two decimal places. 8) f() = A) 7.77 B) C) 0.06 D) ) 9

10 Answer Ke Testname: PRACTICE FOR THE EXAM ( ) 1) discriminant ) ± b 3) -b a 4) quadratic inequalit ) completing the square 6) (0 k) 7) (h 0) 8) (h k) 9) quadratic formula ) quadratic 11) A 1) D 13) A 14) D 1) B 16) C 17) B 18) B 19) B 0) D 1) D ) C 3) B 4) C ) A 6) B 7) D 8) A 9) C 30) A 31) B 3) A 33) B 34) D 3) C 36) D 37) B 38) B 39) C 40) A

11 Answer Ke Testname: PRACTICE FOR THE EXAM ( ) 41) verte (0-3); ais = ) verte (4 0); ais = ) verte (- -3); ais =

12 Answer Ke Testname: PRACTICE FOR THE EXAM ( ) 44) verte (0 0); ais = ) verte (-4 1); ais = ) verte (4 1); ais =

13 Answer Ke Testname: PRACTICE FOR THE EXAM ( ) 47) verte (- 0); ais = ) C 49) D 0) A 1) D ) B 3) C 4) C ) A 6) C 7) C 8) D 13

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