Algebra II Honors Combined Study Guides Units 1-4 Unit 1 Study Guide Linear Review, 3-1, 3-2 & 4-5

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1 Algebra II Honors Combined Study Guides Units 1-4 Unit 1 Study Guide Linear Review, 3-1, 3- & 4-5 Linear Review Be able to identify the domain, range, and inverse of a function Be able to create a relation, mapping, table and graph Be able to determine whether a relation is a function Know the characteristics of linear function (parent form, translated form, graph, domain, and range) Example #1: Use {(, -3), (-3, 4), (, -4), (-3, 0)} to answer the following questions. a. Identify the domain, range, and inverse. b. Create a table, graph, and mapping. c. Is the relation a function? 1b. Example #: Answer the following questions about linear functions. a. What is the parent function? b. What is a general equation for a translated form? c. Graph the parent function. d. What is the domain and range of the parent function? e. Graph the inverse of the parent function. f. Is the parent function one-to-one? c. e.

2 (3-1 & 3-) Solving Systems of Linear Equations Be able to solve a system graphically, algebraically, and using a table Be able to classify a system Be able to set up a system of linear equations and solve a real life situation Example #3: Solve the system of equations using the following table. Example #4: Solve one system algebraically and the other graphically. Classify each system. a. x y 3x 6y 6 b. x y y x 5 (4-5) Matrices: Be able to set up a system, write a matrix equation and use the inverse to solve a system Example #5: Set up a matrix equation for x y z 5 x y z 8. Then solve it using an inverse matrix. x 3y z 1 Example #6: Set up a system of equations, a matrix equation and then solve the system. a. You work at a grocery store. One week you work 0 daytime hours and 0 evening hours and earn $80. Another week you work 30 day time hours and 1 evening hours earn a total of $76. Set up a system of equation to find the daytime and evening rate. b. Concert tickets are $4 for adults, $15 for children and $1 for seniors. The revenue from the concert was $5670. Five times as many adults attended as seniors. Twice as many children attended as seniors. Set up and solve a system of equations to determine how many of each ticket were sold.

3 Unit Study Guide 3-3, 3-4, -7 & -8 (3-3) Linear Inequalities: Be able to tell whether an ordered pair is a solution of a system. Be able to graph a system of inequalities. Be able to write a system of inequalities from a real life situation. Example #1: Tell whether the ordered pair is a solution of the system. a. b. c. Example #: Graph the system of linear inequalities. a. b. Example #3: You are taking a trip with your family. You are going to share driving time with your dad. You are only allowed to drive for at most two hours at one time. The speed limit on the highway on which you are traveling is 65 miles per hour. Write a system of inequalities that describe the number of hours and miles you might possibly drive.

4 (3-4) Linear Programming: Be able to find the maximum and minimum values of an objective function Be able to decide what the objective function and constraints are based on real life situations Be able to use linear programming to maximize or minimize a situation Example #4: Objective Function: C 4x 5 y x 0 Constraints: y 0 x y 6 Example #5: You are sewing doll clothes to sell at a craft show. Party dresses take.5 hours to make while casual sets take 1 hour. You make a profit of $9.00 on each party dress and $4.00 on each casual set. If you have no more than 30 hours available to sew and can make at most 15 outfits to sell, how many of each kind should you sew to maximize your profit? Be sure to identify your variables, show your constraints and the objective function. (-7) Piecewise Functions Be able to evaluate piecewise functions Be able to graph piecewise functions Be able to write a piecewise function from a graph Be able to represent a real life situation using piecewise functions

5 Example #6: Evaluate f (x) when x 4,8,. Example #7: Graph each function. a. x, if x 3 f ( x) b. x 4, if x x 3, if x 0 f ( x) 3, if 0 x x 5, if x 1, if x 1, if 1 x 3 f ( x) 3, if 3 x 6 4, if 6 x 8 Example #8: Write a piecewise function to represent the situation and graphs below. a. Write a piecewise function that gives the admission price for a given age. The admission rates at an amusement park are as follows: Children 5 years old and under: Free Children over 5 and up to (and including) 1 years old: $5.00 Children over 1 and up to (and including) 18 years old: $1.00 Adults: $18.00 b. c. d. What is the domain and range of in part c?

6 (-8) Absolute Value Functions Be able to describe, graph and analyze absolute value functions Be able to create a table and graph the inverse of an absolute value function Be able to write an absolute value equation from the graph Example #9: Describe the transformation of y x 6 3 from its parent function. Then state the 3 vertex, line of symmetry, domain, and range. D: R: V: AOS: Example #10: Use a table to graph y x 4 and its inverse on the same coordinate plane. Example 11: Write an equation of the graph shown. 11 Example 1: The roof line of an A-frame home follows the path given by y x. Graph the 6 function on the calculator. Find the domain and range and then interpret the width and height.

7 Unit 3 Study Guide (5-, 6-3, 6-4 & 6-5) Be able to add, subtract, multiply, divide and factor polynomials. Perform the indicated operation Use synthetic division to divide each polynomial Factor each polynomial completely

8 Unit 4 Study Guide Part I ( & 5.6) (5-1) Quadratic Functions Be able to write quadratic equations in standard form and identify the coefficients. Be able to find the domain, range, vertex and axis of symmetry from standard and vertex form. Be able to describe the transformation of a quadratic function that is in vertex form from its parent function. Be able to create tables and graph quadratic functions & its inverse in standard, vertex, and intercept form. Be able to solve real life problems involving quadratic functions. Example #1: Complete the table. Coeff V Stretch or Shrink Opens Max or Min Vertex AOS Domain Range y ( x ) 1 1 Example #: Describe the transformation of y ( x ) 4 from its parent function. Then state 3 the vertex, axis of symmetry, domain, and range. Vertex: AOS: Domain: Range: Example #3: Use a table to graph each quadratic function and its inverse. a) y x x 3 b)

9 Example #4: Part of a roller coasters path can be modeled by the function is the horizontal distance in feet the roller coaster has traveled and f is its height in feet above the ground. a) What is the roller coasters maximum height above ground on this part of the path?, where x b) How far has the roller coaster travelled horizontally when it reaches its maximum height? c) How far has the roller coaster travelled horizontally on this part of the path when it goes back to the ground? (5.6) Solutions of a Quadratic & the Discriminant ONLY Be able to describe the quadratic solutions from a graph. Be able to use the discriminant to describe the number and type of quadratic solutions. Example #5: Describe the quadratic solution for each graph. a) b) c) Example #6: Find the discriminant and give the number and type of solution of each equation. a) x 14x 49 0 b) 3x 10x 5 0 (5-) Solving Quadratic Functions by Factoring Be able to solve a quadratic by factoring. Know the terms: x-intercept, zeros & roots Example #7: Solve each quadratic equation by factoring. a) x 6x 7 0 b) 4x 1x 0 c) x 3 0 (5-3) Solving Quadratic Functions by Find the Square Roots Be able to solve a quadratic by finding the square roots. Example #8: Solve each quadratic equation by finding the square root. a) 5 x b) x c) x 3 1 3

10 The midterm will include sections