BC: MATH, SHAPES OUR WORLD
FC: Its a beautiful world, this Math world in which we live
1: Graphing Equations To graph an equation is to make a drawing that represents the solution of the equation. X and Y intercepts An x-intercept is a point (a,0) To find a, let y = 0 and solve for x. An y-intercept is a point (0,b) To find b let x = 0 and solve for y. I learned this by substituting 0 for the x value and then for the y value to get my intercepts. Also using the graphing calculator to graph.
2: The Distance Formula The distance d between any two given points such as (-2,2) and (3,-6), replace (3,-2) for your x values and replace (6,2) for your y values in the distance formula I learned this by substituting the points given in the place of x and y, then solve the equation
3: Graph the Function Estimate the Domain and Range by setting the equation to zero. always set the equations to zero to fiind the domain. i also learned to use this by using my domain and range hands.
4: Express numbers in terms of i. I learn this when i saw a negative sguare root, the negative sign can come out as i.
5: Quadratic Function I learned to solve these by moving all terms to the left side and setting equation equal to 0. Then i break the problem down, then i have 2 problems that set to 0 then solve. | (x+1)(2x-3) = 0 x+1 = 0 x = -1 | 2x-3 = 0 2x = 3 x = 3/2
6: Decartes'Rule of Signs | written in descending or ascending order, a polynomial function with real coefficients and a nonzero constant term. I learned that every time the sign changes that will be your first positive even number, then count back that number spaces to get the net integer if it exist. It cannot be a negative number. For negative integers just substitute (-x) in equations Positive P(x) Negative P(-x)
7: A=[9 7] B=[-8 9] [6 2] [6 -4] A+B [1 19] [12 -2] | MATRICES I learned to add matrices by adding each number to the number in the same position in the second matrix that corresponds. When adding or 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
8: Special Completing the Square | i learned to do special completing the square by checking for descending order first, then the integer in position (a) must be 1. i move (c) to the right I multiply (b) times 1/2 , square it, and then add it to both sides. i factor the left side and combine like terms on the right. then take the square root of both sides and solve for to find two answers +(PLUS) and - (MINUS)