SV #1: Unit F Concept 10: Given Polynomial of 4th or 5th Degree, Find all Zeroes (Real and Complex)

This problem is about finding the zeroes and factorization of complex polynomials with the highest degree of 4. In concept 10, we will have either irrational or imaginary numbers as one or more of our zeroes. We will be applying the rational roots and factor theorem, along with Descartes Rule of Signs, to solve this polynomial. Dealing with imaginary numbers is also a useful skill to have. As a result, it is imperative that a student has studied the previous concepts well, as this concept will combine all of them into solving a polynomial to the 4th degree.

A student needs to pay special attention to the synthetic division of the polynomial by one of the possible zeroes. It is crucial to use the next synthetic division bar once he or she has found of the zero heroes. Then, after dividing the 4th degree polynomial twice, the student now has a solvable quadratic polynomial and can easily find the rest of the zeroes in this way.

SP#2: Unit E Concept 7: Graphing Polynomials

This problem is about solving a polynomial with a fourth degree and graphing it. A student needs to factor out the polynomial and find the x-intercepts, in addition to their multiplicities. That way, he or she will know how the x-intercepts act on the graph (through, bounce, or curve).
The viewer needs to pay special attention to the end behavior of the graph to understand the general formation of the graph. Since this end behavior is even positive, both ends of the graph will be pointing upwards. In addition, a viewer needs to pay special to the x-intercepts and their multiplicities to see what the graph will look like in between the two ends: whether the graph will go through, bounce off, or curve out of the x-intercepts. These apply to the multiplicities of one, two, and three, respectively.

WPP 4: Unit E Concept 3: Maximizing Area

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WPP 3: Unit E Concept 2: Path of a "Football"

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SP #1: Unit E Concept 1: Identifying x-intercepts, y-intercepts, Vertex (Max/Min), Axis of Quadratics and Graphing Them

This problem is about algebraically changing a equation in standard form into parent form by completing the square. This way, the equation easier to graph when necessary. Important key points a student needs to find are: the vertex, y-intercept, axis of symmetry, and x-intercepts. There are a number of steps involved in finding the solutions to these problems, but they will make graphing the parabola less difficult and complicated in the end.
A student needs to pay attention to the key point of the graphed parabola, which is the vertex. The vertex can either be the maximum or the minimum of the graph, depending on whether a is positive or negative. It is also essential to remember the axis of symmetry on a parabola, since this will help a student graph more points by reflecting them across the parabola. In doing so, a student will have a better understanding of the parent graph function and the graph itself and be able to have an accurate drawing of his or her equation.

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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