BC: This has been a great semester. | Memories
FC: A YEAR IN REVIEW | Math 171
1: Completing the Square | When completing the square follow these 7 simple steps. 1) Check for descending order. 2) There must be a 1 in the a position. 3) Move c to the right side of the equation. 4) Take b and times it by 1/2. Then square it and add it to both sides. 5) Factor the left side and combine like terms on the right. 6) Take the square root of both sides. Remember to add +- on the right side. 7) Solve for x and find 2 answers.
2: Absolute Value | When solving absolute values remember these few steps: 1) Isolate the absolute value. 2) Split the problem into 2 different problems. 3) Solve for x. 4) Check your solution.
3: Absolute Value Cont. | When solving absolute values remember these few steps (Cont.): 1) After you get your solutions you need to graph them on a number line. 2) Less than and less than and equal to symbols are supposed to overlap on the number line. Greater than and greater than and equal to or supposed to go opposite ways.
4: Finding the LT, LC, and Degree | h(x)=2.4x +5x -x+ 1) In order to find the correct answers you need to have the equation in descending order. 2)Underline the term with the largest exponent. LT: Leading Term LC: Leading Coefficient D: Degree LT: 2.4x LC: 2.4 D: 3 | 2 | 3 | 7 | - | 8 | 3
5: Leading Term Test | We use the leading term test to help figure out the behavior of the equation. If n is even, and a >0: The graph looks like a U with an unknown part in the middle. If n is odd, and a <0: The graph looks like an upside down U with an unknown part in the middle. If n is odd, and a >0: The graph looks like a line going from bottom to top with an unknown part in the middle. If n is even, and a <0: The graph looks like a line going from the top to bottom with an unknown in the middle. | n | n | n | n
6: Descarte's Rule of Signs | Descarte's rule of signs helps us find the number of positive and negative zeros that exist in an equation. When finding the positive zeros we count how many times the sign changes in the equation. When we get the number of the zeros we put it on a number line and go back a positive number and add that to the positive number list. However if the number is less than zero we cannot add it. We cannot have a negative number or zeros.
7: Descarte's Rule of Signs Cont. | Then we do f(-x) and again we count how many times that the sign changes. As we do with the positive zeros we find out how many numbers there are and place them on a number line. Then we go back a positive number and add it to the negative zeros list. However again if it is less than zero then we cannot add it to the list.
8: Matrices | When adding and subtracting matrices, the dimensions must be the same. (rows and columns.) When Multiplying matrices, the columns in the first matrix must equal the rows in the second matrix. 3 * 1 1 * 3 Can be multiplied 3 * 1 2 * 1 Cannot be multiplied, No Solution
9: Parametric Equations | To solve parametric equations: 1) We need to find the rectangular equation you need to solve the first equation. 2) After you solve you substitute it into the second equation. 3) Then you find the corresponding restrictions on x.