12x y (4) 2x y (4) 5x y is the same as

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1 Name: Unit #6 Review Quadratic Algebra Date: 1. When 6 is multiplied b the result is 0 1 () 9 1 () 9 1 () 1 0. When is multiplied b the result is () 7 1 () 7 () Written without negative eponents is the same as () 1 () (). Written without negative eponents 6 is the same as 6 () 6 6 () 1 () 6. The greatest common factor of the monomials and is () () 7 () 7 6. The greatest common factor of the monomials 18a b and 0a b is a b () 1a b () ab () 6a b 7. Which of the following is equivalent to ( )? () () 1 9 () Which of the following is equivalent to ( )? 9 () () + 9 () The Arlington Algebra Project, LaGrangeville, NY 10

2 9. The epression 6 7 simplifies to which of the following? () () 1 10 () 10. The ratio of 6 8 to 8 6 can be epressed as the fraction 6 () () () The epressions ( + ) is equal to which of the following for the values of 1 = and 7 =? 1 () 0 () () 7 1. What is the -intercept of the eponential function = 1( )? 1 () 6 () () 1 1. Which of the following is equivalent to 0? () () 10 () 1. If ( + ) is one factor of ( 0) then which of the following represents another factor of this trinomial? () 6 () + 8 () 8 1. Which of the following represents the trinomial ( 0 60) ( + 10) ( 6) () ( 6)( + ) () ( )( + ) () ( + ) ( 6) factored completel? The Arlington Algebra Project, LaGrangeville, NY 10

3 16. Which of the following sets represents the solutions to the equation + 7 = 0? ( )( ) { 7,, } () { 1,1} () { 7, } () {, 7} 17. The equation + 0=0 has a solution set of {, 0} () { 0, } () {, 0} () {, } 18. Factored completel, the binomial ( 6 )( 6+ ) () ( )( + ) () ( 6) ( + 6) () ( + )( ) 6 would be written as 19. Which of the following represents the area of a square if its side length is given b ( )? 9 + () 9 () 1 0 () A rectangle has a length that is five inches more than its width. The rectangle s area is equal to 0 square inches. Which of the following equations could be used to solve for the width, w, of the rectangle? w + w 0=0 () w + 10w = 0 () w + 0= 0 () w+ w+ 10 = 0 1. Which of the following represents the solution set of the equation = 0? { 6, } () {, 8} () {,1} () { 1, }. Which of the following sets represents the -intercepts of the parabola whose equation is given b = + 1? { 1, } () { 1, 1} () {, 7} () { 7, } The Arlington Algebra Project, LaGrangeville, NY 10

4 . A parabola has -intercepts given b the set {, }. Which of the following could be the equation of the parabola? = + () = + () 9 0 = () = + 0. A parabola has -intercepts given b the set {, 8}. Which of the following could be the equation of the parabola? = 6 16 () = () = 8 () = 16 Part II Answer all questions in this part. Each correct answer will receive credits. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive onl 1 credit.. Algebraicall solve the following equation. = Completel factor the following epression: 7. Completel factor the following epression: Part III - Answer all questions in this part. Each correct answer will receive credits. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive onl 1 credit. 8. Solve the following quadratic equation algebraicall. A correct response with no work shown can receive at most 1 credit. 8 6= 0 The Arlington Algebra Project, LaGrangeville, NY 10

5 9. Find the equation of the parabola graphed on the grid to the right. Show or eplain how ou arrived at our answer. 0. Algebraicall, find the -coordinates onl that solve the linear-quadratic sstem of equations shown below. = and = + Part IV - Answer all questions in this part. Each correct answer will receive credits. Clearl indicate the necessar steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive onl 1 credit. 1. Algebraicall solve the following equation = A rectangle is shown at the right whose length is + and whose width is 1. Find the following quantities in simplest form. + (a) The perimeter of the rectangle. 1 (b) The area of the rectangle. The Arlington Algebra Project, LaGrangeville, NY 10

6 . A rectangle has dimensions such that its length is eight less than twice its width, w. Its area is equal to 90 square inches. Determine its width algebraicall.. Algebraicall, find the intersection points of the line and parabola whose equations are given below. (Note that a correct non-algebraic solution can receive onl up to points.) = + 18 and + = A square has its length increased b inches and its width decreased b inches. The resulting rectangle has an area of 1 square inches. Determine the area of the original square. The Arlington Algebra Project, LaGrangeville, NY 10

QUADRATIC FUNCTION REVIEW

Name: Date: QUADRATIC FUNCTION REVIEW Linear and eponential functions are used throughout mathematics and science due to their simplicit and applicabilit. Quadratic functions comprise another ver important