3) Find the distance for each set of ordered pairs (remember to provide EXACT answers): 5) x 2 + y 2 + 6x 6y + 9 = 0 A) Ellipse (x 1) 2

Transcription

1 Algebra Chapter Review 1) State the Midpoint Formula: State the Distance Formula: ID: 1 Name Date ) Find the midpoint for each set of ordered pairs: a) (1, ), (, ) b) (-, 0), (-, 3) Period c) (, ), (-, -5) 3) Find the distance for each set of ordered pairs (remember to provide EXACT answers): a) (-, 10), (-, 13) b) (-, 5), (-, ) c) (7, -3), (1, ) Classif each conic section and write its equation in standard form. ) = 0 A) Parabola = ( + ) + 1 B) Parabola = ( + ) + 5 C) Ellipse ( + 3) 3 1 = ( ) 5 5) = 0 A) Ellipse ( 1) 5 B) Ellipse ( + ) ( + 5) + C) Circle ( + 3) + ( 3) = = 3( ) ) = 0 A) Hperbola ( 1) ( + ) B) Hperbola ( + ) ( 1) C) Circle ( 1) + ( + ) = D) Circle ( ) + ( + ) 7) = 0 A) Parabola = ( 5) + B) Parabola = ( + 5) C) Parabola = ( + ) + 5 = ( ) P 7Khu0tIaV SRohfVtYwaaCrreX nllvcm. caalklp lrzihgah0tas qreqscelrlvnekdq.0 W qmeardie Ow1iItvhk gionefiifnsigtieh lavlvgcegbjras cv. Worksheet b Kuta Software LLC

2 ) + = 0 A) Ellipse ( 3) B) Hperbola ( 3) C) Ellipse ( 3) D) Circle ( 1) + ( + ) = ) = 0 A) Hperbola ( ) ( + 1) 1 B) Hperbola ( ) ( 1) 1 C) Hperbola ( 1) 1 D) Ellipse ( + ) + ( + ) ( 1) 1 Use the information provided to write the standard form equation of each circle. 10) Center: (1, 0) Radius: 7 11) Center lies in the first quadrant Tangent to, =, and = 3 Use the information provided to write the verte form equation of each parabola. 1) Verte at origin, Focus: ( 0, 1 ) 13) Verte: (0, ), ais of smmetr: = 0, length of latus rectum 1, a > 0 Use the information provided to write the standard form equation of each ellipse. 1) Major ais is vertical Center: (3, ) Major ais is units long Minor ais is 10 units long 15) Endpoints of major ais: ( 5, ), ( 5, ) Endpoints of minor ais: (0, 10), ( 10, 10) Use the information provided to write the standard form equation of each hperbola. 1) Vertices: (11, 5), (3, 5) Endpoints of Conjugate Ais: (7, 7) (7, 17) 17) Vertices: (, 0), (3, 0) Foci: (11, 0), (1, 0) -- Y YKjuTt7a psgodf1tdwwazr7eh plulce.v M TAVlZl Dri3gXhktFs jrdeksgefryvsedd. TMaLdQeJ uweictzhy DIvnqfuicn1i5tIeF UARlSgaelbBrAa5 vf.f Worksheet b Kuta Software LLC

3 Identif the center and radius of each. Then sketch the graph. 1) ( 1) + ( 3) = 1) = 0 Identif the verte, ais of smmetr, direction of opening, and length of the latus rectum of each. Then sketch the graph. 0) = ( 5) 1) = 0 Identif the center, length of the major ais, and length of the minor ais of each. Then sketch the graph. ) ( ) 5 ( ) + 1 3) = KSuetvaz ssxomfytswcair5eu LLfCg.S 1AmlHlv FroiXgIhst0sQ Hressesr3vgeOd.V 0MCadCeQ ewi3thhh ZIqnBfjitnait0eR lafl3g1ewbrkau 1K.3 Worksheet b Kuta Software LLC

4 Identif the vertices, length of the transverse ais, and length of the conjugate ais of each. Then sketch the graph. ) 5 ( + ) 5) = 0 Find the eact solution(s) of each sstem of equations. ) a) + = 5 + = 5 7) a) + = 3 + = 3 ) = = 5 ) 3 = Solve each sstem of inequalities b graphing. (remember to attach our graph paper to the review): 30) < > - 31) z mkruftnaq hscomfgtqwasroeb VLjLRCZ.7 q mahlpla JrciYgmhtLsw qrmefsqejruvueqdh.t R KMWaGdMeV wjikthy EIEnsfriEnzitbeO AAQlUgYeibWrad b.b Worksheet b Kuta Software LLC

5 Algebra Chapter Review ID: 1 Name Date Period 1) State the Midpoint Formula: ) Find the midpoint for each set of ordered pairs: (5/, ); (-5, 3/); a) (1, ), (, ) b) (-, 0), (-, 3) State the Distance Formula: The dot net to the choice indicates that it is the answer. c) (, ), (-, -5) 3) Find the distance for each set of ordered pairs (remember to provide EXACT answers): a) (-, 10), (-, 13) b) (-, 5), (-, ) c) (7, -3), (1, ) 3units, 0 units, 1 units Classif each conic section and write its equation in standard form. ) = 0 A) Parabola = ( + ) + 1 B) Parabola = ( + ) + 5 C) Ellipse ( + 3) 3 1 * = ( ) 5 5) = 0 A) Ellipse ( 1) 5 B) Ellipse ( + ) ( + 5) + *C) Circle ( + 3) + ( 3) = = 3( ) ) = 0 A) Hperbola ( + ) *B) Hperbola ( + ) ( 1) ( 1) C) Circle ( 1) + ( + ) = D) Circle ( ) + ( + ) 7) = 0 *A) Parabola = ( 5) + B) Parabola = ( + 5) C) Parabola = ( + ) + 5 = ( ) LKiutOa Skolf1tbwtatrve LLbCd.F o dablolx rr5iggnhtwsl rtezsheprpvhe3db.r a M3a5dUef mwiftcho qignmfsi5ngihtceb AflkgNetbzrqaN g0.v Worksheet b Kuta Software LLC

6 ) + = 0 *A) Ellipse ( 3) B) Hperbola ( 3) C) Ellipse ( 3) D) Circle ( 1) + ( + ) = ) = 0 A) Hperbola ( ) ( + 1) 1 B) Hperbola ( ) ( 1) 1 *C) Hperbola ( 1) 1 D) Ellipse ( + ) + ( + ) ( 1) 1 Use the information provided to write the standard form equation of each circle. 10) Center: (1, 0) Radius: 7 11) Center lies in the first quadrant Tangent to, =, and = 3 ( 1) + = ( ) + ( 3) = 3 Use the information provided to write the verte form equation of each parabola. 1) Verte at origin, Focus: ( 0, 1 ) = 13) Verte: (0, ), ais of smmetr: = 0, length of latus rectum 1, a > 0 + Use the information provided to write the standard form equation of each ellipse. 1) Major ais is vertical Center: (3, ) Major ais is units long Minor ais is 10 units long ( 3) 5 ( + ) 1 15) Endpoints of major ais: ( 5, ), ( 5, ) Endpoints of minor ais: (0, 10), ( 10, 10) ( + 5) 5 ( 10) 1 Use the information provided to write the standard form equation of each hperbola. 1) Vertices: (11, 5), (3, 5) Endpoints of Conjugate Ais: (7, 7) (7, 17) ( 7) 1 ( + 5) 1 17) Vertices: (, 0), (3, 0) Foci: (11, 0), (1, 0) ( ) 1 -- u KquhtRa tslo0fktwzakrwev blbloc.5 r 5AUlkl RrWikgohotGsa 3rSe1sBeGrQvGeVdQ. YM0apdbe Uwniktbht tirnofcidnmiltiei taklgnenbrza IM.P Worksheet b Kuta Software LLC

7 Identif the center and radius of each. Then sketch the graph. 1) ( 1) + ( 3) = Center: (1, 3) Radius: 1) = 0 Center: (, ) Radius: 1 Identif the verte, ais of smmetr, direction of opening, and length of the latus rectum of each. Then sketch the graph. 0) = ( 5) Verte: (, 5) Ais of Sm.: = 5 Opens: Right Latus rectum: 1 units 1) = 0 Verte: (3, ) Ais of Sm.: = 3 Opens: Up Latus rectum: 1 unit Identif the center, length of the major ais, and length of the minor ais of each. Then sketch the graph. ) ( ) 5 ( ) 1 Center: (, ) Major Ais: 10 units Minor Ais: units 3) = 0 Center: ( 3, 1) Major Ais: 10 units Minor Ais: units -3- YKduJtIaV DSWofStOwUacrAe mllcl.q w balrln FrGingqhftpsw PrAesie5rnvKeDdc.3 Q HMuadHea lweiqt0hm wianfhianiictlen DAClNgYeabLrnaH Ds.z Worksheet b Kuta Software LLC

8 Identif the vertices, length of the transverse ais, and length of the conjugate ais of each. Then sketch the graph. ) 5 ( + ) Vertices: (5, ) ( 5, ) Transverse Ais: 10 units Conjugate Ais: units 5) = 0 Vertices: (0, 1) (0, 5) Transverse Ais: units Conjugate Ais: 10 units Find the eact solution(s) of each sstem of equations. ) a) + = 5 + = 5 7) a) + = 3 + = 3 (0, 5); (0, -5) (0, 3); (( 3, 11 ) ; ( ( 3, 11 ) ) = = 5 (, 3), (, -3), (-, 3), (-, -3) ) 3 = no solution Solve each sstem of inequalities b graphing. (remember to attach our graph paper to the review): 30) < > ) K NKBuPtYaC rswoqfmtwbarcef LoLTCn. DALlclO 0r0i5gUhmtTsS ZrDezsleBrnvAeqdI. f MJatdte UwiztIhm RIBnFfWiNnaittneN paglqgeobsrtam q.g Worksheet b Kuta Software LLC