Honors Algebra 2 Unit 8 ~ Bits & Pieces

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1 Honors Algebra Name Unit 8 ~ Bits & Pieces Day Date Topic Assignment(TBD) Wed. May Thurs. May Fri. May Tues. May 7 Wed. May 8 Thurs. May 9 Fri. May 0 Mon. June Tues. June Wed. June 4 Thurs. June 5 Review of completing the square, distance and midpoint formula, and Circles Packet p. 5 Test Corrections Review: Polynomials, Radicals, Compositions Review: Logs AND Rationals Monday, May 6 Memorial Day Review: Piecewise Functions Study for the last Quiz Quiz(Counts as a double Quiz grade) Function Review Parent,Transformation, Domain & Range Function Review Parent,Transformation, Domain & Range Mastery Review (STUDY!!) Mastery Review Test Final Common Exam Review Final Common Exam Review In Class: Released NCFCE Friday, June 6: EXAMS Begin: GOOD LUCK!!! Handout: Packet # Problems #- Handout: Packet # Problems #-68 Handout TBD Packet p. 6 & 7 Review Packet # EVEN Mastery Review Review Packet # ODD Review Packet # EVEN Review Packet # ODD: STUDY!! Homework Average for this unit:

2 Review of Distance and Midpoint Formulas The distance between two points with coordinates (x, y ) and (x, y ) is d ( x x ) ( y y ) If a line segment has endpoints at (x, y ) and (x, y ), then the midpoint of the line segment is: x x, y y Practice:. Find the distance between each pair of points with the give coordinates. a. (-4, 9) and (, -) b. (, 4 ) and (, ). Find the midpoint for each segment if the coordinates of the endpoints are: b. (-5, ) and (-, -7) b. (6, -5) and (-, -7) Practice: Work the problems and then check answers. Part A: Work #-6 Part B: Work #-5

3 H. Algebra Section 0. ~ CIRCLES Definition: A circle is the set of all points in a plane at a distance ( ) from a given point called the. If the circle has its center at the origin, the equation is of the form. However, not all circles have their center at the origin. We can use the distance formula to find the equation of a circle that has its center as (h,k) and radius r I. STANDARD FORM Therefore, standard form of a circle is. Use this to write the equation of a circle with radius, centered at (-, ). Write an equation of a circle with radius, centered at (4, -). Graph this circle after finding its radius and center: ( x ) ( y ) 5 Use the same concepts and formula to write the equation of each of the following: (THINK!) ) A circle whose diameter is 8, and has been translated units left of the origin and 5 units down. ) A circle whose center is (5,.6) and which has a circumference of 4. ) A circle whose radius is 5, has a center of (x, ), and which passes through (,8).

4 II. EXPANDED FORM from our lab, you saw the expanded form of a circle. We need to be able to go back and forth from standard form to expanded form. *To go from standard from to expanded form,. *To go from expanded form to standard form,. Put these in standard form and graph: x x y 4y 0 x y 6x y 0 0 x y x 0 0 x y x 4 9 x x 84 y 6y 4x 4y 4y 8 0 4

5 Unit 8 Circles Match each equation to its graph.. (x + ) + (y ) = 9 A. B. C.. (x ) + (y + ) = 9. x + (y ) = 6 4. x 8x + y 8y + = 0 D. E. F. 5. (x ) + (y + ) = 6 6. (x + ) + y = Find the center and the radius of each circle. 7. (x + ) + (y ) = 6 8. x + (y + ) = (x 5) + y = 0 Write the equation in standard form of the circle with the given center and the given point. 0. Center: (, -). Center: (0, 4). Center: (0, 0) Point: (, ) Point: (5, 4) Point: (0, -4) Write the equation in standard form by completing the square.. x + x + y + 6y + 6 = 0 4. x + 8x + y 4y + = 0 Sketch the graph of the equation. (Graph on graph paper). 5. (x ) + (y + ) = 6 6. (x + ) + y = 5 7. (x + 4) + (y ) = 8. (x ) + y = x + (y + ) = 4 0. (x ) + (y + ) = 9. Given the equations: y x and y x Find the distance between their intersection. 5

6 Write an equation for each translation. Also indicate the domain and range for the translation. Graphing Transformations Sketch the graph of the functions. State the domain and range and tell how they changed from the parent graph.. y x 4 5. y x 6 6. y x 7. y ( x 4) 6 8. y x y x 4 7 6

7 On a sheet of graph paper, graph each equation. Identify the asymptotes. Remember to also sketch the asymptotes. Extra: Create a problem from one of the 8 parent functions that has a vertical compression or stretch, a reflection, and both horizontal and vertical translations. You must identify the parent function, the transformations, and the domain and range. Parent Function Transformation Function Transformations Domain and Range 7

8 Mastery Review for 4 th Quarter ) Sketch a graph of each function below. Clearly mark any asymptotes or holes. f (x ) = Hole(s): x + 6 x - x - Vertical Asymptote(s): Horizontal Asymptote: ) The expression (x +6x -0x -)represents the volume of a square pyramid. The expression (x - ) represents the height of the pyramid. What expression represents the side length of the base? Hint: The formula for the volume of a pyramid is V Bh ) Given the following graph, find the zeros, state their multiplicity and write the polynomial function of least degree. State the if the degree is even or odd and the sign of the leading coefficient. Polynomial of least degree: Circle one Degree: EVEN ODD Leading Coefficient: POSITIVE NEGATIVE 4) Write an equation for a circle in standard form given: End points (4, -) and (7, 5). 5) What are the roots of 5x 8 ( x )? 6) Write an equation for a circle with a diameter that has endpoints at (, -8) and (-, -4). 8

9 7) A computer store offers a 7% discount off the list price x for any computer bought with cash, rather than put on credit. At the same time, the manufacturer offers a $0 rebate for each purchase of a computer. What is the difference between the two compositions? 8) Given the function f (x) = (x - ) + find: a the domain and range of f(x) b) f - (x) c) f - (0) 9) Given f ( x ) x x x and g( x ) 4x evaluate f(g(x)). 0) Solve 6 x 4.5 x ) Troy s parents started a savings account for him when he was born. They invested $00 in an account with 8% annual interest compounded quarterly. How much is in the account on his 8 th birthday? ) Suppose you invest $050 at an annual interest rate of 4.5% compounded continuously. Find the amount in the account after 6 years. ) Jane purchased an antique lamp. The value of the lamp has been falling and rising as described by the polynomial function V ( x) x 90x 50, where x is the number of year since the lamp was purchased. What is the y-intercept of this function and what does it represent? 4) Solve log 4 x log 4 log 4 5 5) Solve logx (log 4 log) 6 6) Solve x 8 4 x 7 9

10 7) If p varies directly as the square of q and inversely as the square root of r, and p = 80 when q = 4 and r = 49, find p when q = 8 and r = 44. 8) Suppose y varies jointly as x and z. Find y when x = 6 and z =, if y = 8 when = and z =. 9) Find all of the zeros for f(x) = 6x + 5x 9x + 0) What is the polynomial function of least degree with integral coefficients that has 9 and ( + i) as its roots? x x ) Find the sum: x x x 5x 4 9 ) Find the difference: x 7x x 4 x ) Divide: 5x 5 x 6x 9 0x 0 x 4) Simplify: 5 6 5) Solve: x x 0