4th Quarter-PBAEnd of Year Project

Erin Clare Burke 1st period

*We’re going to play a game . Take the first letter of each thing in the picture (starting on slide two) and figure out the puzzle at the end to find out where I want to live! Wahoo! Go Algebra projects! Also, some pictures may be hidden by wonderful Algebra, work carefully.

Five Things to be Successful in Algebra 2

• Do your homework/practices • Pay attention in class• Don’t get behind• If you don’t understand, ask questions or go to

tutorials • If you fail everything else, just make sure you

do well on tests because they’ll replace other grades

Quarter 1: 1.2 Functions and Relations• A function is a relation in which

each input has one output.• A relation is a set of inputs and

outputs, often written as ordered pairs (input, output). Can also be written as a mapping diagram or graph.

if every vertical line you can draw goes through only 1 point, y is a function of x . If you can draw a vertical line that goes through 2 points, y is not a function of x . This is called the vertical line test.

Fails vertical line test (above)

Passes vertical line test (above)

If each input has only one line connected to it, then the outputs are a function of the inputs.

X is a function of Y, Y is not a function of X

-2 6

-1 10.7

0 14.5

1 16.3

1 17.9

This in not a function

{(-2,4), (-1,9), (0,8), (1,- 9), (2,-4)} this is a function

Quarter 1: 1.3 Domain and Rangex > 4 X can be any number greater

than 4, but it cannot be 4

6 ≤ x < 10 X can be any number greater than 6 (including 6), and less than 10 (not including 10)

h > 7 h can be any number greater than 7, cannot be 7

8 < y ≤ 16 y can be any number greater than 8 (not including 8) and less than or equal to 16

Domain: (- ∞ ,2] or x ≥ 2 Range: (-∞, ∞) or all real numbers

Domain is the limit of the x values and range is the limit of the y values.

Quarter 2: 3.5 Factoring

Look for a GCF (greatest common factor) first.If the first number is negative, factor out -1.

Make sure your equation is in standard form (ax 2 + bx + c).

4x 2 + 12x + 5=

Any number of terms

GCF

2 terms Difference of squares (a2 – b2 = (a + b)(a – b)

3 terms Factor mentally (first and last multiply, what multiplies and what adds to get the middle term)

4 terms Factor by grouping

(2x + 5)(2x + 1)

x2 – 4x2 – 4 = (x )(x )x2 – 4 = (x – 2)(x + 2)

x2 – 16 x2 – 42

x2 – 16 = x2 – 42 = (x – 4)(x + 4)

x2 + 4x – x – 4 x2 + 4x – x – 4 = x(x + 4) – 1(x + 4)= (x + 4)(x – 1)

x2 – 4x + 6x – 24

x2 – 4x + 6x – 24= x(x – 4) + 6(x – 4)= (x – 4)(x + 6)

Quarter 2: 3.11 Quadratic Formula and Discriminant•Always set equation to 0

first•Some quadratic equations cannot be factored•No decimals •Discriminant= b² − 4ac

Discriminant # of Roots Type of Roots

Negative 2 Imaginary

Positive and perfect square

2 Real, Rational

Positive and non-perfect square

2 Real, Irrational

Equals 0 1 Real, Rational

Quarter 3: 4.8a Solving Radical Equations 1. Isolate the radical term2. Square (or cube, etc.)

both sides3. Solve for x4. Check for extraneous

solutions

√x + 2 + 4 = 7√x + 2 = 3( √x + 2 ) 2 = 32 x + 2 = 9x = 7Check:√x + 2 + 4 = 7√7 + 2 + 4 77 = 7

√x - 12 = 2 - √x√x - 12 = 2 - √x( √x - 12 ) 2 = (2 - √x ) 2x - 12 = 4 - 4 √x + x-16 = -4 √x4 = √x16 = xCheck:√x- 12 = 2 - √x√16 - 12 2 - √16√4 2 - 42 ≠ -2The solution does not check, so the equation has an extraneous solution.

This one’s tricky! Hint: think of The Little Prince

Quarter 3: 4.9 Solving Radical Inequalities

1. Solve for x2. Solve for when the

radicand is greater than 0

-When taking the square root of the radicand it can never be a negative number and it always has to be greater than 0.

*Remember when multiplying or dividing by a negative, flip the inequality symbol.

Quarter 4: 6.5 Properties of Logarithms To expand logarithmic expressions Log Rules1) logb(mn) = logb(m) + logb(n)2) logb(m/n) = logb(m) – logb(n)3) logb(mn) = n · logb(m)In words:1) Multiplication inside the log can be turned into addition outside the log, and vice versa.2) Division inside the log can be turned into subtraction outside the log, and vice versa.3) An exponent on everything inside a log can be moved out front as a multiplier, and vice versa.

log3(2x) = log3(2) + log3(x)= log3(2) + log3(x)log4( 16/x ) = 2 – log4(x)

log5(x3)= 3log5(x)

Use the laws of exponents to condense logarithmic expressions

Quarter 4: 6.6a Solving Log Equations

Change of Base Formula:Log Argument= Exponent base

OR exponent

Base = Argument

Solve each equation for x

log2(x) = 4 24 = x 16 = x

log2(8) = x

2 x = 8 (8 = 23 )

2 x = 23 x = 3

log2(x) + log2(x – 2) = 3 log2((x)(x – 2)) = 3 log2(x2 – 2x) = 3 23 = x2 – 2x 8 = x2 – 2x 0 = x2 – 2x – 8 0 = (x – 4)(x + 2) x = 4, –2 *logs cannot have 0 or negative arguments so

x =4

5.10 Solving Rationals

Work/Job(1/you) + (1/me) = (1/us)Distance/RateDistance/Rate A/ (+,-,=) B/ = t

Solving Rations is relevant to my life in that each of my siblings and I have jobs to do around the house. Every once in a while, one of us will get a rather large job, such as cleaning out the garage. To get it done in time for us to be able to do whatever we want that day, we group up with one another to complete said job quicker. This is like the work/job formula. Through this, we finish our jobs in significantly less time than it would take to do ourselves. This makes us happy so we all have to take turns helping each other out.

Well we’ve made it! And, I’m assuming you got it right. So, congratulations! The place I

want to live is Beyin Beach, Ghana.