Mth Quadratic functions and quadratic equations

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1 Mth 0 - Quadratic functions and quadratic equations Name Find the product. 1) 8a3(2a a) 2) ( + 4)( + 6) 3) (3p - 1)(9p2 + 3p + 1) 4) ( )( ) ) (4a - 7)2 Factor completel. 6) ) 0a4b - 32b3 8) ) u2-4uv - 32v2 ) ) ) Solve the equation. 13) 24d2 + 38d + 1 = 0 14) m2-9m = 0 1) = ) ( - 6)( - 8) = 288 Use the square root propert to solve the equation. All solutions are real numbers. 17) (7t + 2)2 = 13 18) (4s + 9)2 = 4 19) z2 + 3 = ) (4 + )2 = -8 1

2 The two graphs shown represent the graphic solution to what equation? What are the approimate solutions to the equation? What are the eact solutions to the equation? 21) Solve the equation. 22) 3n2 = -12n ) z 2 3 = z ) = -6 For the net three problems use the discriminant to determine whether the following equation has solutions that are: two different real solutions; eactl one real solution; or two different imaginar solutions. 2) s2-7s - 8 = 0 26) w2 + 3w + = 0 27) = 0 Answer the question. 28) Describe how the graph of = is shifted compared to the graph of = 2. For the net two problems, find the coordinates of the verte of the parabola. 29) = ) = Identif the verte of the quadratic equation. 31) f() = ( + ) ) f() = ) f() = ( - 8)2 Tell whether the graph opens upward or downward and whether the graph is wider, narrower, or the same as f() = 2. 34) f() =

3 For the net two problems identif which graph matches the equation. Do not use the calculator, eplain how ou decide which one is the graph. 3) Do not use the calculator, eplain how ou decide which one is the graph. f() = ( + 4)2 + 3 A B 36) f() = ( - 2)2-4 A B Sketch the graph of the parabola. 37) f() =

4 38) f() = -4( - 2) The calculator screen shows the -intercepts of the graph. Use the graphs to solve each equation. 39) = 0 40) = 0 Answer the question. 41) The graph of a quadratic function = f() is shown in the standard viewing window, without -ais tick marks. Which one of the following choices would be the onl possible solution set for the equation f() = 0? A) -2, 4 B) -4, 2 C) -2, -4 D) 2, 4 4

5 Graph the parabola. Use the coordinates of the verte and two more points. 42) = ) = Choose the equation that matches the graph. 44) - - f() = , f() = f() = , f() =

6 4) - - Solve the problem. = , = = , = ) John owns a hotdog stand. He has found that his profit is represented b the equation P() = , with P being profits and the number of hotdogs. a) How man hotdogs must he sell to earn the most profit? b) Sketch the graph of the function. Don't use the calculator. Now check with the calculator and indicate the window values used. c) Find P() and eplain the meaning within the contet of the problem. d) How man hotdogs must he sell to earn more than $80? Solve graphicall. Eplain how ou use our calculator to solve. Label the points that help ou answer this problem. 47) An object is thrown upward with an initial velocit of 14 ft per second. Its height is given b h = -14t2 + 6t at time t seconds. a) After how man seconds does it hit the ground? b) Sketch the graph using our knowledge. Then use the calculator to check. Indicate window values used. Label aes. c) Make up three different questions related to this problem. Answer them. 48) Bob owns a watch repair shop. He has found that the cost of operating his shop is given b c = , where c is cost and is the number of watches repaired. How man watches must he repair to have the lowest cost? Make up 3 different questions related to this problem and answer them. A bo is standing on a flat field and tosses his ball toward a second bo standing at the other end of the field. The path of the ball is a parabola, and the equation of the path is = ) What is the name of the place on the path where the ball is highest from the ground? 0) What is the highest the ball will be above the flat field and for what value of? 1) How man -intercepts are there on the graph of the equation? Find them 6

7 2) What are the points on the parabola called where the ball is at ground level? Decide whether the ordered pair is a solution of the given sstem. 3) (6, 1) + = 7 - = Solve the sstem using the graphing method. 4) + = = Solve b the elimination method. ) + 2 = = -4 6) = = 4 7) 3 - = = 20 8) -4-6 = = -6 Use the substitution method to solve the sstem of linear equations. 9) + 2 = = - 60) 3 + = = -8 61) + = = -7 7

8 Solve the problem. 62) The table shown was generated b a graphics calculator. The functions defined b 1 and 2 are linear. a) Based on the table, find the coordinates of the point of intersection of the graphs. b) Find the equations for Y1 and Y2. (Are the linear? Wh?) c) Solve b an method to check our answer to part (a). 63) The solution set of the sstem 1 = - + and 2 = is {(2,3)}. Which of the two calculator generated screens, left or right, is the appropriate one for this sstem? 64) Which of the ordered pairs listed could be possible solutions for the sstem whose graphs are shown in the viewing window of a graphics calculator? Answer the question. A) (-16, -7) B) (-20, 12) or (16, 7) C) (16, -7) D) None of the listed pairs is a possible solution. 6) What is indicated b the occurrence of a false statement such as "0 = 1" when ou solve a sstem of two linear equation (in two variables) using elimination? 66) What is indicated b the occurrence of a true statement such as "0 = 0" when ou solve a sstem of two linear equation (in two variables) using substitution? 67) Graphs of two linear functions f and g that are neither parallel nor coincident intersect in how man points? 8

9 Answer Ke Testname: REV-PARABOLAS-2.TST 1) 16a a + 96a23 2) ) 27p3-1 4) ) 16a2-6a ) (3 + 2)(3-2) 7) 2b(a2 + 4b)(a2-4b) 8) ( + 2)( - 3) 9) (u + 4v)(u - 8v) ) (3 + 2)(3 + 4) 11) (4 + 3)( + 3) 12) 2( - 3)( + 4) 13) - 3 4, ) 9, 0 1) {8, 7} 16) {, 24} 17) 13-2, ) - 7 4, ) {, -} 20) i 8, - - i ) - 19, 19 22) , ) -1, 2 24) = -7 ± i ) Two different rational solutions 26) Two different imaginar solutions 27) Eactl one rational solution 28) The parabola is shifted 9 units to the left. 29) (4, 1) 30) (-4, -8) 31) (-, 7) 32) (0, -4) 33) 8, 0 34) Downward, wider 3) A 36) B 1

10 Answer Ke Testname: REV-PARABOLAS-2.TST 37) ) ) -6, 3 40) -2., 1 41) A 42) - - 2

11 Answer Ke Testname: REV-PARABOLAS-2.TST 43) ) f() = ) = ) 29 hotdogs 47) 4 sec 48) 36 watches 49) The verte 0) Highest height = 4 when = 1 1) 2 2) The -intercepts 3) Yes 4) ) {(-, -7)} 6) {(0, 1)} 7) Infinitel man solutions 8) No solution 9) {(0, 1)} 60) {(, -2)} 61) {(7, -7)} 62) (2, 7) 63) Right {(-4, 6)} 64) C 6) The sstem is inconsistent. 66) The sstem h as an infinite number of solutions. 67) One 3

14.1 Systems of Linear Equations in Two Variables

14.1 Systems of Linear Equations in Two Variables 86 Chapter 1 Sstems of Equations and Matrices 1.1 Sstems of Linear Equations in Two Variables Use the method of substitution to solve sstems of equations in two variables. Use the method of elimination