Sunday, September 29, 2013

SV#1: Unit F Concept 10: How to Find All Real & Complex Zeroes FromPolynomials of 4th or 5th Degree

This problem is about how to find all zeroes (both real and complex) when given a polynomial of the 4th or 5th degree. In this problem, one must find the p's and the q's of the polynomial and and then utilize Descartes Rule of Signs. Afterwards, synthetic division is applied to determine any or all real zeroes, and to reduce the polynomial to a quadratic. In order to find the complex zeroes, one can either factor or plug in the values of the quadratic into the Quadratic Formula.

In order to understand how to solve such a problem, the viewer needs to pay attention to the steps taken to find all of the possible real zeroes. This is important because it enables them to narrow down from literally an infinite amount of possibilities. Another thing the viewer needs to pay attention to is how to rewrite the complex zeroes after using the Quadratic Formula.

Friday, September 20, 2013

SP#2: Unit E Concept 7: Graphing Polynomials with Multiplicities and End Behavior

This problem is about factoring a polynomial and determining its end behavior. In addition, the problem asks us to find the y-intercept and the multiplicity of the x-intercept(s). Using all the information gathered from the original equation, we graph the polynomial on a coordinate plane.

In order to understand how to successfully complete the problem, one must pay attention to the first term and degree of the equation. These parts of the polynomial are crucial because they enable someone to determine the end behavior of a graph. Another thing someone should be wary of is the multiplicities of the x-intercepts. They determine how the graph acts around the x-axis: 1=through; 2=bounce; 3=curve.

Tuesday, September 10, 2013

SP#1: Unit E Concept 1: Identifying and Accurately Graphing the Parts of a Quadratic

This problem is about identifying the different parts of a quadratic in standard form and graphing them accurately. The parts of the graph of a quadratic include: vertex, x-intercepts, a y-intercept, and an axis of symmetry. In order to graph a quadratic easily, one must first change if from standard form to parent function form.

In order to understand how to accurately graph a quadratic, the viewer needs to pay special attention to the steps of completing the square. It is through that process that the quadratic is rewritten in parent function form. Using the values of h and k in the parent function equation, the viewer can obtain the vertex and the axis of symmetry. Another thing the viewer should pay attention to is how to how to get the y-intercept. This can be done by plugging in O for x in the original function. The last thing that the viewer should be aware of is that you can find the x-intercepts by solving the simplified version of the function that is reached after completing the square.