SV 5 Unit J Concept 3-4 - Solving three-variable systems with Gaussian E...

Pay special attention when subtracting your rows because you might end up with an incorrect difference. If you put an incorrect answer you cannot solve for the system correctly. Also, pay attention to what type of system you end up with. Since we ended up with an inconsistent system, we have no solution.

SV4 Unit I: Concept 2: Graphing logarithmic equations

     Pay attention to your equation used when plugging it into your y equals screen. Be sure to use the change of base formula to convert your equation and then plug it in into the y equals screen. Also, make sure you exponentiate your log and to the other side when solving for your y-intercept.

SV#3: Unit H Concept 7: Finding logs given approximation

     Pay attention to factoring the fraction's numerator and denominator down correctly making sure they are your clues given. After you have factored your numerator and denominator  condense your clues into one log, multiplying each clue on the top and bottom. Expand your log using your clues using the properties of logs and make sure each number has one log in the problem. Be sure you bring down the power over to seven. Substitute all the values, or letter, given from your expanded problem.*Please excuse my pauses from 3:39 to 3:50*

SV#2 Unit G Concepts 1-7- Graphing a Rational Function

The problem shows you how to graph a rational function when the degree is bigger on top and one bigger than the bottom degree, meaning that it has no horizontal asymptote and it has a slant asymptote. In this problem, you perform long division in order to get your slant asymptote equation in slope-intercept form that gives you your first two points for the graph. Cross off any common factors from your factored equation and your remaining factor's zero is your VA equation. Plot any holes from the equation, any crossed off common factors equal to zero then for your y-value you must plug in your x-value into the simplified equation, not the factored. We found the domain of the equation: the x-value of my vertical asymptote. The x-intercepts are found by plugging zero for y using the factored equation, canceling the denominator, then setting the numerator's factors equal to zero. For the y-intercept plugging in 0 for all of the x's and solving  factor the numerator and denominator of the function  Be sure to graph all of the pieces on the graph: sketch asymptotes (slant/vertical), plot any holes, plot x-intercept and y-intercept and tracing any other needed points for the graph.

Pay attention when factoring your numerator and denominator, making sure it's not incorrect otherwise you will not graph the rational function right. Remember that we do not include our remainder from long division into our slant asymptote equation, you must plug in the x-value into the simplified equation to get the y-value meaning you do not use your factored equation. Make sure you put parenthesis around your correct rational function when inputting in your calculator tracing to get other values. Be sure to sketch your graph correctly, not to cross through the vertical asymptote.

SV#1 Unit: F Concept: 10: Given polynomial of 4th or 5th degree, find all zeroes (real of complex zeroes)

This video demonstrates an example problem on finding zeroes of a polynomial of 4th degree. We list out all possible real/rational zeroes (p's and q's). Then we use Descarte's Rule of Signs to find out how many possible positive and negative real zeroes there will be. We use the Factor Theorem and start trying to find remainders of zero (zero heroes) using a number from the p/q list. Continue to find zero heroes until your reduce your polynomial to a quadratic. Once you have a quadratic, factor it using the quadratic formula.

Remember to take out a GCF from your quadratic before using the values inside the parenthesis into your quadratic equation. Break down your square root (if you can) and in your remaining factors you should distribute the GCF if there are any fractions.