## Sunday, September 29, 2013

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

What is this problem about?
This problem utilizes rational roots theorem and Descartes' Rule of Signs. It is similar to Concept 6 but this time we find all real and complex zeroes. This makes it a bit more difficult to solve since we are now dealing with a possibility of imaginary zeroes and harder quadratics formulas to solve once that step is reached.

What does the viewer need to pay special attention to in order to understand?
The viewer needs to pay special attention to every tiny detail because it is very possible to make a mistake in Descartes' Rule of Signs or some other step. They should also pay special attention to imaginary numbers and always remember they come in conjugates. Be sure to carefully factor the x's that come out of quadratic equations.

**also try to watch the video on full screen or on youtube for best viewing
OH and thank you for watching!

## Sunday, September 15, 2013

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

1. What is this problem about?
This problem allows us to see how polynomials behave at extremes, in the middle, where their highest and lowest points are, where their intercepts, under what intervals they are increasing or decreasing. But most of all the multiplicities of the zeroes show us how to act around the x-axis.

2. What do you need to pay special attention to in order to understand?
Be sure to pay attention to the leading coefficient and its exponent to make sure what direction(s) your end behavior will go off in. Also look at the multiplicities of your zero, these have everything to do with the graph. They determine whether the line will go through, bounce off, or curve through the x-axis. Make sure to find your y-intercept as that will also help develop the line.

## Monday, September 9, 2013

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

1. What is this problem about?

This problem is a quadratic one, where our sketches will be more accurate and detailed. Our equation starts off in standard form: f(x) = ax^2 + bx + c. But to make it easier to graph we complete the square to put in parent function form: f(x) = a(x - h)^2 + k. This form allows us to find the vertex(max/min), axis, y-intercept, and two x-intercepts much easier and more efficiently.

2. What do you need to pay special attention to in order to understand?

Be sure to correctly write out your steps along the process. To find your parent function form, you begin to complete the square by subtracting 1 from both sides. Continue completing the square by using (b/2)^2 to get 2(x + 2)^2 = 7. To get the parent function form you subtract 7 and your equation is 2(x + 2)^2 -7. You then find your y-intercept by plugging 0 in for x to get y=1. Vertex is (h,k) so that would be (-2, -7). Please note that the x-coordinate is -2 not 2 because h is the opposite of the equation when graphed. Your axis of symmetry is also x=-2 which divides the parabola perfectly in half and in a perfectly symmetrical fashion. You find your x-intercepts by solving 2(x + 2)^2 = 7 and you will get x= -2 +/- square root of 7/2 which will help the symmetry with the plotting of extra points to make the graph even more accurate.