Math12

Today in class we reviewed summations. The Greek capital letter, Sigma( ∑) tells us to find the sum of something. We use Summation Notation to evaluate the sum. The number above the Sigma represents the last number in the sequence. The i=number below the Sigma represents the first number in the sequence. And finally, the value to the right of the Sigma represents the operation we preform to each number in the sequence. Everything gets added together to get the final sum. Similarly, we  learned that when given a sequence of numbers, we can write the value of it in Summation Notation. To do this, it is important to look for any patterns, or something in common in all of the numbers, and to notice the highest and lowest numbers. This information allows us to write a set of numbers in Summation Notation. We also learned how to be able to find specifically the first, second, third, fourth etc. values of a sequence, by simply plugging in an n value. Likewise, we used a Recursion, to find the first x amount of values of a sequence.

I tag Dan K.

Today in class we learned how to complete the square for parabolas. First, separate the X and Y values, moving the value not squared to the other side. Next, you add the blanks to each side, but there can not e a number in front of the squared X or Y, so if there is, take the GCF and take it out. Then find the Vertex, the P value ( 4P= X ). Graph and find the directrix and the Focus.

I tag Juliane

Tags: freeze tag, Johannahk

Today we discussed how to solve come up with a rectangular parabola’s standard form equation after given different forms of information. Some given information might be: location of vertices, location of focii, length of major axis, length of minor axis. We use this information to create a formula; for example: if I am given that the length of the major axis is 4, and I am given that the vertices are at (-2,0) and (2,0) then since the center is exactly between the two vertices I know that the center of the graph is at (0,0)

I tag Johanna

In class today, we learned how to graph rectangular hyperbolas. There are two types of hyperbolas: horizontal and vertical. They have very similar standard forms, which can make them easy to mix up. We also learned the equation for asymptotes and eccentricity. When graphing a hyperbola, first you find the center, next you calculate the a and b by taking the square root of the denominators. When you have all your points, draw a dotter rectangle by connecting the points. After that your draw dotter diagonal lines from the center and though the corners of the rectangle. These lines give you your asymptotes. Next you draw your hyperbola according to weather the formula says it’s vertical or horizontal. Lastly, plot your foci, to show whats pushing in curve of the hyperbola. Hyperbolas are a little more confusing than circles and ellipses, but I think with enough practice it will become pretty simple.

I tag Matt G.

today in class we reviewed the topics we have been going over recently for a quiz tomorrow.  some of those topics include finding the center of a circle, finding the radius of a circle, graphing a circle from standard form and general form, finding the center of an ellipse, identifying the a, b, and c  of an ellipse, graphing an ellipse from standard and general form, how to calculate the eccentricity for both, and how to use given information such as the foci or vertices to write an ellipse in standard form. i thought the review we did today helped a lot because even though this is relatively simple math, it is easy to make a small mistake so this just helped me to fine tune my skills at this topic. examples of all the topics for this unit gave me good practice and preparation for the quiz tomorrow.

i tag: dan k

Today in class we reviewed for the test that we have tomorrow in class. The topics on the test include completing the square, long division, synthetic division, identify polynomial functions (and by their graph), Descartes rule of signs, rational root therem, using zeros- finding an nth degree polynomial equation, identify a polynomial equation using a graph, and sketching a graph using an equation. We learned many different topics in this unit. The one topic i found to be the easiest is synthetic division i find it easy to do and its very straight forward. the topic i found the hardest in this unit was descartes rule s of signs. I thought it was very tricky but when we did enough examples of it i got the hang of it. And the review sheet we got in class really helped me to prepare for the test because it showed what exactly is on the test and i was able to check all my answers with the answer sheet we got.

I tag: Samantha W

Today in class we reviewed how to graph even and odd functions. The rules differentiating between negative and positive odd and even graphs can get a little confusing, but after the worksheet we did in class i felt a lot more confident. For example, positive negative graphs always have both ends pointing down. We also reviewed completing squares.  When completing the square, you always add the C value to the other side of the equation. Then you leave space for the value of (B/2)^2 on both sides. Then you factor the equation to get the negative and positive values of x. Even and odd functions as well as completing the square will be on our test on wednesday.

i tag shannonf

Today we learned how to write polynomial functions and determine the end behavior of the graph.  In doing this, we had to review the rules for an equation of a line.  A line can either go right or left.  This is found out by the equations degree.  If the degree is 1, the line will go through the x-axis.  If the degree is even, the line will touch the x-axis and then turn around.  And if the degree is odd and greater than 1, the line will eventually plateau.  If you follow these rules you will be able to determine the equation of a line based upon a graph.

I tag Sarah Q.

Tags: AdamY

Today in class, we used Decarte’s Rule of Signs and the Rational Root Theorem to solve for the variable in the function. After figuring out the possible combinations of positives, negatives, and imaginary numbers, using the Rule of Signs, we use the Rational Root Theorem. In doing this, we take the factors of the constant and divide by the factors of the leading coefficient. Then we test each of those values using Synthetic Division until we get a remainder of zero. When we get a remainder of zero, we rewrite the function and solve for x.

I found the process of solving these types of problems to be lengthy, and a little hard to understand, but after doing a lot of practice problems, the whole procedure becomes a lot easier to understand.

I tag Frank M.

Today we learned Descartes’ Rule of Signs for finding the zeroes of a polynomial, assuming that you don’t have the graph to look at. It will not tell you where the polynomial’s zeros are but will tell you how many roots to expect. To solve problems first look at the polynomial in the positive case, for example:

f (x) = x⁵ – x⁴ + 3x³ + 9x² – x + 5

Count how many times the signs change from negative to positive or positive to negative. There are four sign changes in the positive case so four is the maximum possible number of possible zeros for the polynomial. Next, we look at f (–x), so the sign of x is in the negative case. There is only one sign change in the negative case so there is one negative root. The number of total roots must add up to the exponent on the first x in this case 5. There is 4 positive roots, 1 negative root, and zero imaginary roots. To find another prediction of roots subtract either the positive or negative by an even number. In this case we can subtract 2 from the positive root and have 2 positive roots, 1 negative root, and 2 imaginary roots. A third scenario we can have is by subtracting the positive by 4 and having 0 positive roots, 1 negative root, and 4 imaginary roots.

I tag Juliane N