Saturday, September 28, 2013

SV#1: Unit F Concept10: Finding all real and imaginary zeroes of a polynomial

Student Video#1 is about finding all the real and imaginary zeroes of a quartic or quintic polynomial. This includes the process of listing out all possible real/rational zeroes(p's and q's), finding out how many possible positive and negative real zeroes there will be by using the Descartes' Rule of Signs, finding zero heroes using a number from your p/q list or graphing calculator. Once you find a zero hero, you now use your answer row with a degree lower as a new header and keep on dividing it until your polynomial is a quadratic. Once you get a quadratic formula you take a GCF if possible and factor or solve using the quadratic formula.

The viewer needs to pay special attention to all the positive and negative changes when synthetic dividing because adding when supposed to subtract or vice verse really will make you get wrong polynomials and make it harder to find zeroes. Also, the viewer needs to pay special attention to distributing the negatives correctly when using the quadratic formula because then the numbers will not come out and the equation will not make any sense. All these precautions should be taken to get the correct answer and save time because when you get something wrong it takes time to look over your work trying to find mistakes.

Saturday, September 14, 2013

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



       This problem is about graphing a fourth degree polynomial in standard form. Once, we factor out the equation we set the factors equal to zero and then we get our x-intercepts also  known as zeroes. We needed to include the multiplicity of each zero.
       Multiplicity is just how many times that order pair comes up in the graph and how you are going to approach that order pair(straight through, bounce off, or curve). Then, this problem called for the y-intercept, which is found by plugging x=0 to every x in the original equation. Lastly, to find the end behavior you look if the leading coefficient is positive or negative and look if the biggest degree is even or odd.

Monday, September 9, 2013

WPP#3: Unit E Concept 2: Quadratic Applications (Path of Football)


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

This problem is about taking a quadratic equation in standard form and changing it to get it into parent function form. We change it by moving the last number to the other side and then factoring out anything if possible. Then, we add the magic number to both sides. We get the magic number by dividing b(the middle number) by two and then taking the answer and squaring it. Then, we take the perfect squares of the quadratic equation with the magic number. In other words, by completing the square.
  Graphing a quadratic equation is way easier if it is in parent function for because we can get the vertex and everything else quickly. The vertex is the h and k in the parent function form(f(x)=a(x-h)^2+k. By using the parent function form we can make sketches more accurate and detailed. The viewer needs to pay special attention to foiling out a two and remembering to put that two to the other side and then multiplying first with the magic number and then adding/subtracting the number that was already there.