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

         


            Hello my name is Ivan and today we will be solving a polynomial with real and complex roots. This problem is a fourth degree polynomial which we must find the roots for. To begin, we will use Descartes Rule of Signs to find the number of all the possible positive or negative roots. Following that, you find all the possible real zeroes using the p's and q's. Now that we have an idea of where to start, we can use synthetic division to find a zero hero using the Factor Theorem. Our graphing calculator can give us a shortcut to do this, if needed. Once a zero hero is found, that is the first zero and you can continue using synthetic division with the answer row to try the rest of the possible roots until you condense down into a quadratic. From there, you can use the quadratic formula or try to factor it yourself with your favorite method, if possible.

            The viewer must pay special attention to the answer they obtain. In the end, there should be four zeroes, since the degree of our polynomial is four. Also, the viewer can find an answer more quick by using a graphing calculator to find a zero hero. To do this, go to "2ND", "CALC", "ZERO", "LFTBOUND", "RTBOUND", and your calculator will yield results. Make sure every step in synthetic division is correct, or else you can miss a valuable zero hero. Pay special attention to fractions because they can be confusing to work with while doing synthetic division.

                                                                                   THANK YOU!

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

          This picture presents a polynomial and executes the solutions needed to find its properties, including: x-int, y-int, zeroes (with multiplicities), end behavior. You must find the x-intercepts (with multiplicities), y-intercept, and identify end behavior. With those values, you must graph your polynomial and make sure it corresponds with your findings. The steps to the problem are shown on the top and the answers are in the bottom portion of the picture. The arrows correspond to the parts you may look at if you are stuck on your own.

           Note that the extrema and intervals of increase and decrease do not need to be found, they are there if you need help in determining how far to go when creating the "humps" of the graph. Make sure to factor all the way through so your zeroes match the degree of the polynomial. Also, make the factors equal to zero so you get the right value. List the multiplicity of each zero even if it only shows up once.

WPP#4: Unit E Concept 3 - Maximizing Area

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WPP#3: Unit E Concept 2 - Path of Water Polo Ball

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

In this concept we will be identifying x-intercepts, y-intercepts, vertex (max/min), axis of quadratics and graphing them. The quadratic is in standard form.This picture illustrates the process involved in finding the parts to a quadratic function. The parent function, vertex, y-intercept, axis of symmetry, and x-intercepts must be found using the standard form.

 Realize that the quadratic is facing downward because the "a" value is negative. Also, when completing the square, make sure the right value for "b" is kept and no improper change is made, specially when taking out the "a" coefficient. Use a calculator to find the x-intercepts. Good Luck!

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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