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

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This video will go over how you can find all the real and complex zeroes of a polynomial. It will draw upon your knowledge from Descarte's Rule of Signs, your p's/q's, synthetic division, and factoring.

You need to pay close attention to when you are factoring, so you can get all the right signs and numbers, when you are using synthetic division, and well basically everything. This is the type of problem that if you get 1 tiny detail wrong, the rest of your answers will be wrong as well.

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

Equation:

f(x)= x^4-5x^3+3x^2+9x

This problem is about is to see if you can use what you know about polynomials to make an accurate graph of it.  To solve it, you must need to know and understand how to factor a polynomial, the end behavior of certain polynomials, how to find the x-intercepts with multiplicities, the y-intercept, and how to graph the zeroes.

If you want to make your graph even more accurate, then you can find and use the extrema of the graph. In addition, be careful to make sure the end behavior is correct and the zeroes are correctly plotted. If a zero has a multiplicity of 1, then the graph goes through the point. If a zero has a multiplicity of 2, then the graph bounces off the point. Finally, if the zero has a multiplicity of 3, then the graph curves through the point. Make sure that all your zeroes match up to the highest degree (exponent).

1. Since we chose the zeroes(x-intercepts) first, multiply all the factors to get the equation.

2. Make note of the end behavior and how the graph will approach a zero (Thru, Bounce, Curve).

3. Find the y-intercept by plugging in 0 for x in the equation and plot it.

4. Draw the graph.

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

Problem: 

F(x) = 6x² + 13x - 8

This problem is to see if you can identify the x-intercepts, y-intercepts, vertex(max/min), axis of quadratics and how to graph quadratics using the parent function. Already, just by looking at this problem, you already know that the graph opens up because a is positive.

To continue, you must remember how to complete the square, so you can convert it from standard form to the parent function equation, which would then make it easier for you to graph the function. After that, you can easily solve for x-intercepts, y-intercepts, vertex(max/min), and the axis of symmetry. Be careful with the x-intercepts because sometimes you might have imaginary numbers, but you wouldn't plot it on a graph because there is no axis for them.

Work:

Parent function equation:

y = 6(x + 13/12)^2 - 361/24

Vertex: (-13/12, -361/24) min.

Y-intercept: (0, -8)

X-intercept(s): 

(½, 0) and (-8/3, 0)

or

(0.5, 0) and (-2,67, 0)

After you finish the work, all you have to do is to plot the points on the graph and exploit symmetry to graph the quadratic (as shone below).

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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