SV#1: Unit F Concept 10 - Finding all real and imaginary zeroes of a polynomial

*warning: There's a little noise throughout the video but it shouldn't be too distracting. Sorry for the inconvenience.* Our problem is about finding imaginary and irrational zeroes on top of finding real zeroes, which are accounted for in Decarte's Rule of Signs and our P/q's. It is important to remember to not include certain fractions in our p/q's because we may have already written the reduced form of it already. It is also good to remember that in Decarte's Rule of Signs, that we must account for irrational or imaginary zeroes by writing "3 or 1" real zeroes. A helpful step is also to take out a GCF from the quadratic (after finding 2 zeroes) because it makes smaller, nicer numbers for when we plug them into our quadratic formula. Concerning writing factors, remember to multiply x by the number of the denominator of the irrational zero so we have the entirety of it over one number. It is also good to remember to distribute any GCF we took out previously, to a factor that contains a fraction.

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

This problem is about being able to sketch a relatively accurate graph when given a polynomial. We are able to get an idea of how the graph should look because after factoring, we are able to find and plot the x-intercepts/zeroes, the y-intercept, as well as identify the end behavior (if the graph goes up when we move left, if it goes down, etc. Also, looking back at the zeroes, we should be able to identify the multiplicity of each point, and determine whether the graph will go through (multiplicity of 1), bounce (multiplicity of 2), or curve (multiplicity of 3). To go a step further and create an even more accurate graph, we would find the extremas (min and max) and the intervals of increase and decrease to determine the behavior in between the end behaviors.

A few things that would make graphing these polynomials easier would be to pay attention to end behavior as well as remember that you are only able to go through the x-axis through a point. If you know how the end behavior looks for each kind of graph (even positive, even negative, odd positive, odd negative), you will know where to start and where to end. Also, knowing that you are only able to go through the x-axis through the points, helps us create an accurate graph with little to no mistakes. A trick to remember to go through the points is to think that the x-axis is a wall. Those points are doors. We cannot walk through walls. See my point? (PUN NOT INTENDED... UNTIL NOW.)

WPP#4: Unit E Concept 3 - Maximizing Area

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WPP#3: Unit E Concept 2 - Path of Football (or other object)

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SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

        This problem is allowing us to understand how to change a standard equation into a parent function. This will make our lives that much easier because all needed points in a graph are visible in this equation. In this problem, you are to find the vertex, y-intercept, axis, and x-intercepts. Many steps are taken in order to find these answers. However, the steps will make graphing easier and accurate for us.

        Special things to pay attention to include the (h,k) within the parent function. The formula for a parent function is y = a(x-h)^2 +k. Remember that the "h" will be the opposite of its sign. Also, we should remember that in x-intercepts, imaginary numbers occur (as seen in this problem), in which case, you are unable to graph the function. 

WPP#2: Unit A Concept 7 - Profit, Revenue, Cost

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WPP#1: Unit A Concept 6 - Linear Models

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