Prerequisites: Solving Equations

methods for solving quadratic equations

1. Factoring 2. square roots 3. Completing the square 4. Quadratic formula.

solving absolute value equations

1. Isolate absolute value 2. set up two equations 3. solve each equation

solving absolute value inequalites

1. Isolate the absolute value 2. decide if its an AND or an OR 3. AND = < -c < x < c 4. OR = > x > +c or x < -c 5. solve inequalities 6. write answer in interval notation and use union for an OR.

solving a formula for a variable

1. Mult by LCM, 2. Distribute if necessary 3. get all variables on one side that you need 4. factor the GCF 5. get variable by itself

solve linear equations

1. Multiply by LCM to cancel fractions 2. Distribute 3. Combine like terms 4. get x by itself

solve rational equations

1. Multiply by LCM to cancel fractions. (Only on top) 2. all fractions should be gone. 3. solve equation left. 4. check solutions against excluded values

interval notation

1. Parentheses () represent NOT including the value 2. Brackets [] include value

solving inequalities

1. Solve for x like an equation if u divide or multiply by a negative switch signs. 2. write in interval notation

Simplifying Radicals

Look for the biggest perfect square that divides evenly. ex: 50= (25 & 2 which leads to 5 and 5 and 2 so 5 square root of 2)

when to solve by completing the square

When a = 1 and b = even. remember add (b/2)^2 to both sides x2 + bx + ------- = -c + -------

Properties of Exponents

When you multiply powers of the same base you just add the exponents (a+b) when you raise a power to a power (x2)^4=x8 Raise a product to a power (xy)^2=x2y2 If you divide powers of the same base then you just subtract the exponents. any number raised to the zero power = 1 Negative exponents always means the reciprocal of the positive exponents

Point Slope Equation

Y-Y1= M(x-x1)

Interval Notation

[1,2] (1,2)

when to solve by factoring

only factor if u can do it quickly A = 1

Parallel/Perpendicular

parallel lines same slope perpendicular lines have reciprocal slope

when to solve by square roots

when there is no "bx" term. or when a squared factor ex: (x+1)^2

when to solve by quadratic formula

x= -b (+-) squareroot b2 - 4ac/2a