Fibonacci Haiku: True Friend Jorge :D

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SP #4: Unit J Concept 5: Partial Fraction decomposition with distinct

The important keys to remember when solving factors is substituting in letters (A, B, ..) and to also combine like terms. The use of the letters A and B are to separate the denominators. The combining like terms divides the problem up in a way that is easier to understand. One must also remember to solve for the values by using elimination or substitution.

SV #5: Unit J Concept 3: Solving three-variable systems with Gauss-Jordan elimination/ matrices/ row-echelon form/back-substitution

The important key things to remember when doing matrices is to work out the problem carefully. The simplest negative or positive can ruin the entire matrix and force you to start all over. To make sure you got the right answer you plug in the equations into the calculator.

SP #5: Unit J Concept 6: Partial Fraction Decomposition with Repeated Factors

In these first steps, the viewer must pay attention to the common denominator. The denominator must be the same for the entire function meaning, the viewer must foil the necessary functions to fit with the common denominator.

Next, the viewer must follow the foiling steps closely, for the tinniest mistake can lead to a wrong answer. After foiling, the next step is to combine the functions together under the common denominator, and equal it to the original function. From here we cancel out the denominators and combine like terms.

Once we have combined like terms,we solve for each variable. The viewer can choose to solve for the variables with ether elimination, or substitution. I chose elimination. Once you find your first value, you plug it in with another function, and solve for the next variable. Finally, with 2 values found, the viewer plugs in the values with the last variable and solves to find the last of the three values. Finally, we put the values into the A/(x-1)+ B/(x-2)+ C/(x-2)^2 function.

Finally, we compose the function to check if it is correct!

WPP #5: Unit I Concept 3; Compund Interest

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SV #3; Unit I Concept 2; Graphing Logarithmic functins and identifying x-intercepts, and y-intercepts, asymptote, domain, and range

Graphing Logarithmic equations requires a lot more work than graphing a simple y= equation. The trickiest parts would most likely be finding the x-int. and y-int. In order to find the x-intercept we need to equal the entire equation to 0 and solve from there. In order to find the y-intercept we need to replace the x with a 0 and solve from there. When solving for a Logarithmic equation, it is required to cancel out the log by equaling both sides with the same base. From there and on, everything is pretty simple.

SP #3; Unit I Concept 1; Graphing exponential Functions and Identifying x-intercept, y-intercept, Asymptote, Domain, and the Range

Graphing exponential Functions and Identifying x-intercept, y-intercept, Asymptote, Domain, and the Range includes a few tricky steps. the trickiest step is knowing how to find the x-intercept and the y-intercept. when solving for the x-intercept, one must remember to equal the y to 0. when solving a rule to remember is that there cannot be a negative ln When solving for a y-intercept, one must remember to equal the x to 0. Another rule to remember is that the log (base) answer cannot be a negative.

SV # 3; Unit H, Concept 7: Solving logs Using Approximations

The trickiest, and most important parts to remember about these equations are the rules of exponents. When inputting the log into the equations the proper way to set the exponent is to move it to the front of the log. Another important issue is knowing when to add a negative into the equation. when anything is divided by a number, the first number of the denominator must be changed to a negative because it rotates from the bottom of the division problem into a regular, line equation.

SV #2; Unit G Concepts 1-7: How to solve Rational Functions

In Unit G, we find the slant, vertical,and horizontal asymptotes, as well as it's holes. You first determine whether the graph is a horizontal or slant asymptotes, it can not be both. with either asymptote you would then have to find its holes, if it consists of any, x-intercepts, y-intercepts, domain, and a vertical asymptote. There are specific steps to solving for each item, so pay close attention to the short video of how to solve for a Slant Asymptote. Many key points to remember about this unit, it how to solve for each item. A horizontal asymptote has a bigger degree on the bottom (denominator), while a slant asymptote has a bigger degree on top (numerator). A hole is found when something is able to cancel with the factored out equation. A vertical asymptote is found when equaling the denominator with zero. If there is a Hole, we simply remove the "hole" from the equation. these are the main important issues to focus on when solving a polynomial.

SV #1; Unit F Concept 10; Given polynomial of 4'th or 5'th degree, find all zeros

f(x)= same signs brought down. f(-x)= EVEN degrees stay the SAME, and ODD degrees CHANGE. This problem is about finding the zeros of a quartic polynomial. In order to d=find the zeros to a quartic polynomial, one must combine all the previous concepts from unit F into one problem. One starts with finding how many possible zeros there are from the equation and how many possible(+)zeros and possible(-) zeros there are in the equation. Finding the zeros from then on requires patience in choosing a possible zero to plug into the equation to determine if it ends to equal a ZERO HERO. Once you minimize the equation to a quadratic, we use the quadratic formula because we know that, in this unit, we will be solving for imaginary numbers. As a viewer, one must pay close attention to the signs used in the equation and how to change them when changing them into a factorization. Another important thing to remember is the quadratic formula, and when to use it. If the quadratic equation is factorable, the quadratic formula is not needed. One must also remember to distribute the imaginary numbers with (x-)and to multiply the (x-) with a common denominator.

SP #2: Unit E Concept 7; Graphing polynomial, including: x-intercept, y-intercept, zeros, end behanior. All polynomials will be factorable

In these problems we are to graph polynomials, including x-intercepts, y-intercepts, zeros (with multiples), and end behaviors. First, you must try to factor out the GCF of the equation, if not you continue solving and find your end behaviors. Knowing your end behaviors you now know how your graph will look and where the end points will point to. Next, you solve to find your x-intercepts and their multiples. Then you plug in a zero into the original equation to find your y-intercept. At this point, we need to find our extrema's: max, and min. An their intervals of increase and decrease. Finally, you plug in your x-intercepts into the graph and use the rules of multiplicities to draw the directions of the graph.  

In these problems you have to keep in mind the rules of end equations as well as the x-intercepts and their multiplicities. Also a very important thing to keep in mind is the rule if multiplicities. Those rules determine whether you go through the x point, bounce from it, or curve as you go through it. 

SP #1: Unit E Concept 1; Identifying x-int., y-inter., vertex, axis of quadratics and graphing them.

This Problem is about identifying the x-intercepts, as well as the y-intercept, vertex (max/min), axis of quadratic and to also graph them. This problem is about finding the parent function which leads you to finding the vertex, as well as the y-intercept, and axis point. the x-intercepts are found with the parent graph. Once you interpreted your parent graph, you then solve to find your x-intercepts. From this point you are able to draw your graph.

WPP #4, Unit E Concept 3; Finding maximum and minimum values of quadratic applications using calculator

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WPP #3' Unit E Concept 2; Finding max. and min. values of quadratic applications using claculator

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WPP #2:Unit A Concept 7; Writing ans solving cost, revenue, and profit word problems

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WPP #1; Unit A Concept 6; Writing linear models and evaluating for word problems

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