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

*Sorry I stuttered a lot!
This problem is about finding zeroes of a 5th or 4th degree polynomial. Throughout the unit we have learned the steps into finding the zeros which will all be incorporated in this video. By using the rational roots theorem, Descartes Rule of Signs, synthetic division, and quadratic formula, we can find the zeros of the polynomial.

You will need to pay special attention to each step because they are all crucial into finding your zeroes. In the rational roots theorem, remember that it's p over q and not the other way around. For the Descartes Rule of Signs, be sure to change the signs only on numbers with a odd numbered degree. Don't forget that we count down by 2's so we can account imaginary numbers! For synthetic division, even if you don't get zero hero in your first try, don't be disappointed, just use other numbers and eventually you'll get zero heroes and get your equation to a polynomial where you will either factor or use the quadratic equation.

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

This problem is about being able to sketch a graph with the given polynomial. By factoring the equation and setting the factors equal to 0 to solve for zeroes, we can find our points in order to graph it. Besides finding out our x-intercepts and  y-intercepts, we also need to know our end behaviors (how the graph acts at the extremes). We can identify the end behavior by examining our leading coefficient (whether it's positive or negative) and the degree (whether it's even or negative). There are four types of end behaviors (even positive, even negative, odd positive, and odd negative). Not only do you need to know the end behaviors but also the zero's multiplicity so you know how it acts around the x-axis, this is where TBC-123 comes in handy. To accurately sketch the graph, we can also find our extremas, the minimum and maximum, and the intervals of increase and decrease.

To make sure you're doing all this accurately, you should pay special attention to your factors and end behaviors. If you can't factor your equation correctly, then your zeros will come out different and not precise. Also, the end behaviors must be the correct so make sure you have the song and dance moves memorized so you know how the graph will look like! Lastly, you should make sure you have the TBC-123 down. If there's a M of 1, that means the graph will go THROUGH the point. If the M is 2, then the graph will BOUNCE off the point. Then if your M is 3, your graph will curve through the point. Remember that each point is a door and it's the only way you can get through the x-axis. If there isn't a point (door) there, that means it's just a wall and you can't walk through a wall!

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

This problem is about identifying the four main parts of a quadratic on a graph. These main parts are the x-intercepts, y-intercepts, vertex (max/min), axis of quadratics (and graphing). This example will show you how to change the quadratic to a parent function equation and will also show you how to graph the quadratic in the end. Also, we will be completing the square so hopefully you haven't forgotten how to do that!

In order to understand how to identify the parts and be able to graph this, you must pay special attention to how you complete the square and getting the correct information on the right (the parent function equation, vertex, etc.) in order to accurately graph the quadratic.

The first step you need to do is to add 10 to the other side, cancelling the 10 on the left. You will then have 2x^2+8x=10. Take out a two for your coefficient and complete the square. You will be left with 2(x+2)^2=18. For the parent function equation, just subtract 18 from both sides and you will have your equation: 2(x+2)^2-18. At this point you can find your vertex, which is (-2, -18). Plug 0 into 'x' to solve for the y-intercept. The axis of symmetry will be x=h so x=-2. Afterwards add 18 back on both sides from the parent graph equation and continue to solve for the x-intercepts. Since your answers for the x-intercepts are whole number and does not have a radical or anything, that will be your exact & approximate answer. Also, since there isn't any imaginary number, you will be able to graph this and it will touch the x-axis.

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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