Flicked. ,y) (y,x ) 0 YC 2,4 ) tyx ) p=(2, egg. # p '= (-1/2) Station #1 - Rigid Transformations Station

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1 Station #1 Rigid Transformations Station 1) Which graph correctly shows the reflection of rectangle PQRS over the line y x? (a) (b) (X (c) y) (yx ) 0 (d) p(2 p ' (1/2) 1) 2) What is the angle of rotation of the image? 3) Which rule represents the transformation shown? (a) 0 90 CCW (b) 180 YC 24 ) (c) 270 CCW (d) 360 Flicked tyx ) egg. # " ' B' 2) 0

2 Station #2 Dilations and Composite Transformations 1) Which of the following single symbolic rules combines a reflection across the line y x followed by a translation 3 units to the left and 2 units down? A. (x 3 y 2) B. (y 2 x 3) 0 C. (y 3 x 2) D. (y + 3 x 2) E. (y 2 x + 3) ( a b) ( b a) ( b 3 a 2) 2) The triangle ΔPQR has area 20 square inches. A dilation with symbolic rule ( 1 2 x 1 y) creates an 2 new triangle ΔP Q R. What is the area of ΔP Q R? Show your work! 3) Use the coordinates of TAB T(32) A(11) and B(33) to perform the following composite transformation: a dilation with a magnitude of 2 followed by a rotation of CCW. Draw the T A B image under this composite transformation. (? ' a 20. It 5 ( a b) ( 2 a 2 b ) ( 2 b 2 a) T ' ( 6 4 ) A ' B ( 2 2) ' t 6 6)

3 Station 3: Parallel Lines and Angles 1. 5!"# 10 are a. sameside interior 0b. alternate interior angles c. corresponding angles d. none of these 2. Which of the following is a pair of corresponding angles? a. 0 7!"# 15 b. 2!"# 6 c. 9!"# 14 d. none of these 3. Use the diagram to the right. Complete the proof using your Reasons Bank. Note: Some reasons can be used more than one time and some reasons will not be used at all. Given:!! Given:! 2 +! Prove:!! Statements 1.!! ! 2! ! 2 +! ! 8 +! !"# 15 are supplementary 6. Reasons Given Alternate Def of Congruence Given substitution Def OF Exterior Any Thm Supplementary 7.!! 7. Same side interior Angle converse Thm Reasons Bank Transitive Property Definition of Congruence Definition of Supplementary Angles Corresponding Angle Postulate: If two parallel lines are intersected by a transversal then corresponding angles are congruent. Alternate Interior Angle Converse Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent then the lines are parallel. Alternate Exterior Angle Theorem: If two parallel lines are intersected by a transversal then the alternate exterior angles are congruent. SameSide Interior Angle Converse Theorem: If two lines are cut by a transversal and the sameside interior angles are supplementary then the lines are parallel. Given Substitution Property Linear Pair Postulate

4 Station 4: Intro to Quadratics 1) For the graph shown to the right answer each of the following. R (all real numbers) to 8 ] Domain Range C 30 ) ( 10 ) Zeroes C. I so ) Interval of Decrease C Interval of Increase 1 ) 2) Use the given information to write a quadratic function in factored form. The parabola opens downward and the xintercepts are (5 0) and (22 0). y ( X 5) ( X 22 )

5 Station 5: Vertex Form of a Quadratic 1) Use the following function to answer questions a b and c:!!!! 4! + 3. (a) Find the zeros of the function. (b) Using the zeros you found in part (a) find the axis of symmetry for the quadratic function. (c) Using the information in part (b) determine the vertex of the parabola. (d) Write the vertex form of the function extent XitzX X2 FG )( (2 1 ) y(x 25 : 3

6 Station 6: Transformations of Quadratics and Completing the Square 1) Match one equation from the list below to each of the graphs given. Note: Not all equations will be used. y (x 2) y (x 4) y 4(x + 2) y (x + 2) 2 4 y 4(x 2) y (x + 2) y 4(x 4) 2 2 y 4(x 4) (a) (b) y(x (c) (d) (4) Use completing the square to rewrite ONE function in vertex form and SOLVE another. You only need to pick one for each so you will not use one of the functions. Show all your work! (a) g(x) x 2 + 4x + 13 (b) h(x) x 2 8x 4 (c) m(x) 2x x + 5 (1) EH ) :( 254 g(x)(x' 25 ) ( FCxT#tE' )2 HItIjEf4516mlxt2CX2HOxtEIgKtCxtbzj2t1z@j2glxkLXthE5.4.p L X

7 Station 7: Quadratic Formula 1. Write the quadratic formula (don t forget x ) 2. Solve using the quadratic formula. Solutions should be written in simplest form. (No decimal approximations) XIbt.FI#2aX5IF4iI6 (a) x 2 + 5x 6 0 (b) 2x 2 18x ) l8±tfye t # TO 221 Or ± 5 l8±2fi

8 Station 8: Real Numbers 1) The additive inverse of 6 is:! (a)! (b) 0 (c)o6 2) Which correctly depicts using the multiplicative identity?! (d)! (a) (b) ! (c) 8! 1 (d) 8 + ( 8) 0 3) (a) Distributive Property over Addition (b) Commutative Property of Addition (c) 0 Associative Property of Addition (d) Commutative Property of Multiplication 4) Choose the correct translation for the following mathematical statement. a b ℝ!! ℝ. (a) For all numbers a and b contained in the set of integers a times b is in the set of integers. (b) For all numbers a and b contained in the set of rational numbers a times b is in the set of rational numbers. (c) For all numbers a and b contained in the set of real numbers a times b is in the set of rational numbers. (d) For all numbers a and b contained in the set of real numbers a times b is in the set of real numbers. : 5) What does it mean for real numbers to be closed under division? (a) That when dividing two real numbers the result remains a fraction. (b) That when dividing two real numbers the result is decimal. (c) That when dividing two real numbers the result remains a rational number. (d) That when dividing two real numbers the result remains a real number. : 6) The following mathematical statement disproves which of the following claims: 1 3 2? (a) Natural numbers are closed under addition. (b) Integers are closed under subtraction. (c) Natural numbers are closed under subtraction. (d) Rational numbers are closed under subtraction. Consider the following functions.!! 7!! 2! + 14 ℎ! 5!! + 10!! + 7! 1!! 2!! + 13!!! 4!! Use a separate sheet of paper to work out each problem and circle the letter of the correct answer. 7) What is!! + ℎ!? 8) What is ℎ!!!?! (a) 12! + 15! + 13 (a) 10!! 12!! + 65!! + 130!! + 2!! + 91!! 13! (b) 2!! + 15! + 13 (b) 0 10!! 20!! + 65!! + 116!! + 2!! + 91!! 13! (c) 12!! + 10!! + 5! + 13 (c) 10!! 12!! + 65!! 14!! + 2!! + 73!! + 13! (d) (d) 10!! 20!! + 65!! + 116!! 2!! 73!! 13! 0 2!! + 10!! + 5! + 13

9 Station 9: Complex Numbers 1) Name each of the following for the quadratic function!!! 2 + 6! 16. (a) Zeros (b) Axis of Symmetry (c) Vertex X. ftp.#).6i2fi3tri)t(z.r ;) 7 at X ) Determine the solution set for the quadratic inequality. a)! 2 6! 7 0 ' ho ± ' YEE 's 3) What are the solutions to this system of equations? he a! 2! + 1!! FC } ) : (35+66) IFI 6/23 ( 3 7 ) ;# "or # or a n3 En ] I E zine 2t t 2 1 or (1) +13 ( 13 ) t3 5)