1. Solving linear inequalities and linear equations is very similar. However, there is some discrepancy. Inequality sign changes into opposite when two parts of inequality are multiplied by a negative number. For example,, but. Besides, the solution of a linear equation is a single point while the solution of linear inequality is intervals. For example, we solve linear equation and linear inequality.
2. Quadratic equation can be solved in four ways (Tussy &Gustafson 65). For example, we solve the following quadratic equation: a) by means of quadratic formula:. ;b) by means of factoring. This method is used for solving quadratic equations with coefficient “a” that is equal to one. Two solutions of the quadratic equation should meet the following conditions: their sum must be equal to the coefficient “b” with the opposite sign, and their product must be equal to the coefficient “c”. .c) by means of completing the square: d) by means of factor by grouping:
3. Absolute value inequality.We solve the following inequality: .. Thus, the solution is the union of two intervals:.
For example, we have two conditions and. We combine them into a compound inequality: . The solution of this inequality is the interval (-10, 12).
4. In order to find the equation of the line, we need to know the slope and y intercept.a) It has been known that the slope = 3 and the y intercept is (0, 2). Then the equation of the line can be written in the following way:.b) It has been known that slope = b and one point that belongs to the line (x1, y1). Then the equation of the line is written in the following way: .If the slope = -3 and a point that belongs to the line is (1, 2). Then the equation of the can be written in the following way:.c) If we know two points that are on the line (x1, y1) and (x2, y2), we should initially find the slope: . Then, according to the point b, we find the equation line.
5. Factor by grouping. We consider the following expression: and find the product of ab: . We determine what factors of 6 in an amount equal to b:. Then we write down 5x as the sum of 2x +3 x:
6. The coordinates of parabola vertex can be found by means of the following formulas: For example, we find the parabola vertex. . Thus, the parabola vertex is the point (1, 5).
7. We consider the following rational function and find the domain, range and asymptotes. Since we cannot divide by zero, the domain is all real numbers except point. Range is equal to the domain of the inverse function. We firstly find the inverse function by means of substituting the variable “x” by “y” and then find “y”: . Thus, range f (x) is all real numbers except point. Since the domain f (x) is all real numbers except the point, the vertical asymptote.
8. Compound Interest Formula is written in the following way: .Where P - principal amount; r - annual rate of interest; t - number of years the amount is deposited; A - amount of money accumulated after n years, including interest; n - number of times the interest is compounded per year.
For example: An amount of $ 20,000.00 is deposited in a bank. An annual interest rate is 7 %. It compounded biannually. What is the balance in 3 years? P = 20000 , r = 7/100 = 0.07, n = 2 , t = 3. Find A: Answer: $ 24,585.1
Tussy, A., Gustafson, D. Elementary and Intermediate Algebra (9th ed.). California: Cengage Learning, 2013. Print.