Algebra 2 Fall Semester Exam Review

Test Format Final Exam is all calculator 35 Questions All Multiple Choice

Key Concepts on Test Graphing Parent Functions and their characteristics Domain/Range/Functions Interval Notation and Inequality Notation Transformations –Order of transformations –Graphing using transformations Graphing Absolute Value Functions Solving Absolute Value Equations and Inequalities

Key Concepts on Test Horizontal and Vertical Parabolas –Graphing them given an equation –Finding Key Info (Vertex, Focus, Directrix) –Writing Equations given 2 pieces of info –Complete the Square to convert formats

Key Concepts on Test Linear/Quadratic Regressions (STAT) Data Analysis (Zoom 9) Quadratic Equations –Simplify positive and negative radicals –Simplify Complex Numbers –Factoring Methods –Square Roots Method –Complete the Square –Quadratic Formula

Calculator Can be used to solve 60% of your test Know the following: –How to graph –2 nd trace (zeros and maximums) –Linear & quadratic regressions –Plug in numbers (watch out for negatives)

Testing Hints If you can graph it in the calculator, then do so Double graphing to compare Be careful of negatives when solving equations Questions with graphs! Look carefully at each graph so you select the one you really want Plug in solutions to calculator to check

In Class Review: Today Relations/Functions Domain/Range Transformations Calculator Regression/Data Analysis Quadratic Word Problems

Relations Ordered Pairs (2, 3) (-3, 1) (1, -2) XY Tables Graphs Mapping XY

Example : Given the following ordered pairs, find the domain and range. Is it a function {(4,5), (-2,3), (5,6)} Domain is {-2, 4, 5} Range is {3, 5, 6} YES, no duplicated x-values

Example 1

Example 2

Example 3

Data Analysis Height (meters) Distance Km Zoom 9 What Parent Function?? STAT Plotter “ON”

Weeks Experience Speed (wpm) x-axis y-axis 0

Application Problems Need to change the viewing WINDOW x-min, x-max y-min, y-max

Inverse Concept The main concept of an inverse is the x and y coordinates have switched places

Inverses The inverse of any relation is obtained by switching the coordinates in each ordered pair of the relation. Example: { (1, 2), (3, -1), (5, 4)} is a relation { (2, 1), (-1, 3), (4, 5) is the inverse.

Graphing an Inverse Pick some Critical Points off Original Graph (x, y) SWITCH the x and y values Re-plot the newly formed ordered pairs.

GRAPH the inverse

Inverse Concept The main concept of an inverse is the x and y coordinates have switched places

28 NOTATION FOR THE INVERSE FUNCTION We use the notation for the inverse function of f(x).

Find Inverse of f(x)= 3x + 2 y = 3x + 2 (Replace f(x) with “y”) x = 3y + 2 (Swap variables) 3y = x - 4

Function Composition Notation

Absolute Value Equations

So for this Ex: |x-25|=17 Case 1 (+ case) (x –25) = 17 x=42 Check: |42-25|=17 |17|=17 17=17 Case 2 (- Case) -(x - 25) =17 -x + 25 = 17 - x = - 8 x = 8 Check: |8-25| =17 |-17|=17 17=17

BIG DIFFERENCE Inequalities If you multiply or divide by a negative number then the order of the inequality must be switched.

Solve: |2x+4| > 12 |2x+4| > 12 (2x + 4) > 12 or -(2x + 4) > 12 2x > 8 or -2x - 4 > 12 x > 4 or -2x > 16 or x < -8 Solution set: x > 4 or x <

Parabola A parabola is a set of points in a plane that are all the same distance from a fixed line called the directrix and a fixed point not on the line called the focus.

Key Concept

Vocabulary The perpendicular WIDTH of parabola at the focus point is the LR. LR

Example 1:

Example 2:

Converting to Vertex y = x x + 27 y = (x x + ____) + 27 y = (x x + _36_) y = (x - 6) Vertex Point (6, - 9)

Converting to Vertex