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

In this concept you will be finding the zeroes of a polynomial that is not factorable. Not only that, but you will also find the imaginary zeroes, even though this concept is similar to concept 6, remember that you will be finding imaginary numbers in this concept. You will be using the skills from previous concepts like p's and q's, Descartes's Rule of Signs and synthetic division and a skill from earlier units like either completing the square or using the quadratic formula.




Be careful when doing synthetic division because you might make a mistake if you rush and that can keep you from finding your zero hero resulting in taking a longer time to solve a problem (which is terrible when taking a test). Also be careful when using the quadratic formula, make sure your signs are correct and you have the correct terms in place. Make sure than when you are using the Rule of Signs, you are changing the ones that have a negative exponent and keeping the ones with a positive exponent the same! 

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

Concept 7 is all about graphing polynomials, using the skills from previous concepts you will factor the equation, find the end behavior, find the x-intercepts (as well as the multiplicities), and find the y-intercepts. You may need to find the Extremas and intervals of increase and decrease, but only when instructions tell you to do so. Down below is the problem and the solution.

Problem: x^4 + x^3 - 6x^2 - 4x + 8

Things that you should pay attention to are when you are finding the x-intercepts, please remember that the numbers you see will be opposite, meaning it will be either negative or positive depending on what it is in factored form, as an example: (x-3) will be +3. Also pay attention to if an x-intercept will be a Through, Bounce, or Curve based on its multiplicities.

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

 The problem involves changing an equation from standard form to parent function form: 

f(x) a(x-h)^2 + k. Then from that equation the student must find the x-intercepts, y-intercepts, vertex, axis of symmetry and graph the equation. Using this, the sketch of the equation will look more accurate and detailed. 

When doing this type of problem, it is very important to pay attention when completing the square (to turn the standard equation to parent function form) because when factoring out a number from one side, it must be factored out on the other as well (Step 3). Another important thing to focus on is when you are finding the vertex, the "h" is always opposite from what it is in the equation. Also, it is a good idea to memorize the parent function equation so when facing this type of problem, the student doesn't spend time trying to remember the formula.

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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