Hello Visionaries!

GREAT work on the blog postings...take a moment to browse through all the postings.

Today in class you will be answering the problems from 2 BLOG POSTINGS other than your own. You should post the solutions as a COMMENT - do NOT create a new post. Make sure you type both the question AND answer.

Happy Blogging!
Mrs. Collins

CASE #34: Graphing Rational Expressions

Part 1: Sketching

Directions: Choose 8 problems from your homework worksheet to graph using the graphing calculator. Make sure you write PARENTHESES around the numerator and denominator when you enter them in the gc. In your case journal, write the equation and then sketch the
graph right below it.

Part 2: Analysis

Write a 1 paragraph (5-15 sentences) description of what the graphs of rational functions look like, and how they are different than quadratics.

Introduction: Our topic for this project is vocabulary. As you can see these are the vocabulary words that we learned so far in the year for Math-b. Some of the words that we have gone over will help us understand Math a-lot better. Terms like G.P.S (Given, Plan, Solve) are acronyms they are ways of memorizing certain strategies. Read it, commit it to memory, and math will be a breeze in the near future!

Binomials: algebraic expression of 2 terms
Box method: strategy for factoring trinomials
Coefficient: a number in front of the variable
Constant: the integer in an equation without making it a term
Coordinate: any of a set of numbers used in specifying the location of a point, on a line and surface
Decimal: any real number expressed with a decimal pointDelta: an increment of a variable
Distance: equation evolved from Pythagorean Theorem for finding how much space is between 2 points
Distributive property: distribution of a certain number
Equation: mathematical combination of symbols and numbers with a solution
Expression: a mathematical combination of symbols and numbers
Factoring: operation for resolving a quantity into factors
F.O.I.L: strategy for multiplying like terms in an equation and expression
Fraction: a numerical representation indicating the quotient of two numbers
G.C.F: greastest common factor
G.P.S: given,plan,solve method for solving word problems
Graph: a diagram of horizontal and verticallines, to plot coordinates
integers: any of the natural numbers and negative numbers and zero
Irrational : decimals that never end and never repeatat
linear equations: equion that has the highest exponential term of one
midpoint: halfway mark between 2 points
monomial: algebraic expression with term
natrual: whole numbers positive and negative that are on the number line
negative lead coefficient: number in front of the term with the highest exponent
parallel: lines that are congruent to each other
perpendicular: lines intersecting each other
polynomial: sum of many monomials
quadratic equation: an equation with a highest expontent of 2
rational numbers: numbers that can be expressed as a ratio
simplify: to reduce an equatio/expression or real number to its lowest factor
slope: y=mx+b
terms: the numders or variables in the equationor expression
trinomials: an algebraic expression with 3 terms
variable:a latter or symbol that stands for a number
x-axis: the horizontal line that meets with the y-axis at the origin
y-axis: the vertical line that meets with the x-axis in the origin

Conlusion: these are all the vocabulary words that we have learned in the first marking period. these are the tools you need to suceed in math-b. Use these words wisely.

hey every body yesterday my class to a unit exam. this exam is was made for to see if you are keeping up with your math notes. the exam is given every marking period. well this is my second unit thats i took. the first one i dint do so well. i pretty sure i did well this time because i dont want ot make the same mistake twice. i've been studying very hard with going to tourting and stuff like that. i think this year math is going to be a breez if i keep up the good work. anyways ill catch yall later bye

Our topic is Equation of a Line and Graphing. The equations were based on y = mx + b format. M is the slope, and B is the y intercept. You have to use the coordinates to figure out how to graph the equation. For example y = 3x + b with the coordinates of (1, 2). You would replace x with 1 and b with 2 {2 = 3(1) + b}. Then you would multiply 3 x 1 and then subtract 3 on both sides. Then you divide by 3 on both sides. Finally you graph it.
Equation of a line

Write the slope of the line passing through the two points.
1. (7, 8), (0, 5) m=7/3
2. (-1, 7), (1, 5) m=0/2
3. (12, 1),(36, -42) m=24/-43

Write the y-intercept of the following equations.
y = -3x – 14 y-intercept is -14
y= -x +8 y-intercept is 8


Equation of a line and graphing

Graph the following lines
1. Y=3x+6

Tell if the slope of each equation is positive, negative, zero, or undefined
2. Y=-6x+3
3. Y=7x-4
4. Y=-3x-14
5. Y=-x+8
6. Y=10x-5
7. Y=-5x=7
8. Y=-2/3x=9
9. Y=-1x +5
10. Y=2x+3

In conclusion to this project we would say that this was not the easiest project we were ever assigned. We had to make up equations for the class to solve. Also we had to make up problems of our own and write the slope of the line passing through two points. We had to graph an equation on a graph as an example.

Are you the main factor? {Are you important?}



India Robinson Ashley Holland
Monaisia Livingston





Did you ever have to factor something that didn’t need that much work? Well factoring quadratic equations isn’t really hard. Quadratic is an expression or equation with highest exponent equal to 2. To solve a quadratic equations you have to (1) find the square root of the first and the last term but make sure they can add up to be the middle term. (2)Put the first and the last term together but make sure they can add up to be the middle term.(3) Put the remaining factors together in parenthesis. (4) You should use FOIL (first, outer, inner, & last) to check to make sure your answer is correct.



(1) X^2+8X+16
(2) X^2-10X+25
(3) X^2+14X+49
(4) Y^2-20X+100
(5) X^2+3X-9
(6) X^2-18X81
(7) X^2+12X-144
(8) Y^2-6X+36
(9) X^2+22x+121
(10) X^2+26X+169
(11) X^2+2X-24
(12) P^2+2P-48
(13) W^2+2W-8
(14) X^2-12X+8
(15) X^2-7X+12
..………………………………………………………………………
(11) X^2+2X-24

(X+6) (X-4)
(12) P^2+2P-48

(P-6) (P+8)


(13) W^2+2W-8

(W+4) (W-2)


(14) X^2-8X+12
(X-6) (X-2)


(15) X^2-7X+12
(X-4) (X-3)





This blog posting is about problems that are so simple. It’s about quadratic equations. You don’t have to do much to know how to solve them. All you need to do is be able to recognize square roots. It’s all logic. When you are able to do this it saves you time and space because there is not much to do. If you can do this you can be successful in solving quadratic equations. In the examples that were solved all I did was isolate the first and last terms and simplified them using square roots or finding the factors that give you the middle term and multiply to give you the last term. That’s all there is to it.

For Interest in Our Life's

The are many ways to factor equations or expressions. One of the ways is F.O.I.L. You use this method when you have a trinomial or a binomial. The F in F.O.I.L. means to multiply the first two terms for example if there’s an expression (x + 2)(x – 2) you would multiply the two x’s because they are first in the two terms. The O in F.O.I.L. means outer so you are going to multiply the two outer terms to use the same example with (x+2)(x-2) you will multiply x and -2 because they are the outer numbers in both terms. The I in F.O.I.L. means inner so you are going to multiply the two inner terms in (x+2) (x-2) your are going to multiply 2 and x because they are towards the inside of the equation. Finally the L in F.O.I.L. means last so you are going to multiply the last two numbers in both of the terms for in (x+2)(x-2) you will multiply 2 and -2 because they are the last numbers in both terms.


Examples: To use the problem solving strategy “Foil” to solve.

1. (x-15) (x + 14) = x²-x-210

2. (x – 2) (x – 1) = x² - 3x + 2

3. (dj + 4) (dj + 10) = d²j² + 14dj + 14 or (dj)² + 14dj + 14

4. (L + 12) (L – 4) = L² + 8L – 48

5. (m + 13) (m – 8) = m² + 5m – 104







Examples for class:

1) (x-6)(y+12)=

2) (2x-8)(x+2)=

3) (5qx+10)(4sx+5)=

4) (3q-15)(X-18)=

5) X²-100=

6) 6n²-n-15=

7) X²+11x+30=

8) (2x-4)(x-8)=

9) (x+4) (x+7)=

10) (x+9)(x+3)=




Over all F.O.I.L is an easy strategy to use when it comes to solving trinomials or four terms equations. It’s also a strategy to double check your answer when it’s in parenthesis. F.O.I.L is also better when it has squared numbers, all you have to make sure that before you start if the first and last numbers are perfect squares to reduced it to the greatest common factor to simply it, and if your equation is negative then just turn it back to positive by changing the last too, to the opposite sign if its negative change it positive, and if its positive change it to negative. To finish of F.O.I.L is a very common process used to save time.




By: Dionelis Santiago Rosario, and Jaeleen Guevera

GCF and Perfect Squares!

Group members: Billy Wilson, David Guity, Steven Fernandez

GCF stands for Greatest Common Factor. It’s what we have learned from Elementary School. Simply it’s finding what two numbers have in common and taking it out of both numbers. A perfect square is more complicated. What perfect square is, it’s if a number X can be created by the products of 2 equal number (X=YxY). My group members and I will be writing about how to factor equations or expressions using GCF and perfect squares.

Steps: first you figure out if an expression or equation have either perfect squares are not.

If they do!

Find the square root of the entire equation and square it in the end.
Then find if they have anything in common (GCF) if not than your done.

If they don’t!

Find the GCF of the equation and take out that number from all the numbers in the equation and put it outside the parenthesis.

Example Problems:

1) 5x^2+10x+5 5(x^2+2+1) 5(x+1) (x+1) 5(x+1) ^2

2) 3x^2+6+3 3(x^2+2+1) 3(x+1) (x+1) 3(x+1) ^2

3) 9x^2+4 (3x+2) (3x-2)

4) 16x^2+40x+25 (4x+5) (4x+5) (4x+5) ^2
5) 125x^2+350+245 5(25x^2+70+49) 5(5x+7) (5x+7) 5(5x+7) ^2

Problems for the class:

1.4x^2+9

2.16x^2+144

3.49x^2+121

4.x^2+64

5.196x^2+81

Conclusion

This is the way to factor perfect square. Basically, following the steps will be easy to do. Make sure to check for GCF. There are other ways to factor binomials. This will lead you into the other factoring methods. Hopefully, you can use these steps correctly