Solving Factorable Quadratic Equations
Solving Factorable Quadratic EquationsA quadratic equation is a polynomial equation of degree two. The standard form is ax² + bx + c = 0. There’s no magic to solving quadratic equations. Quadratic equations can be solved by factoring and also by graphing…
Factoring by Grouping
Factoring by GroupingFactoring by Grouping condensed: x² + bx +cFind the product of 1•c.Find two factors of c that add to up to b.Split the middle term into two terms using these factors.Group the four terms to form two pairs.Factor each pair.Factor out…
Closure Property
Closure PropertyA set is closed (under an operation) if and only if the operation on two elements of the set produces another element of the set. If an element outside the set is produced, then the operation is not closed.Example: If you multiply two rea…
Hints for Remembering the Properties of Real Numbers
Hints for Remembering the Properties of Real NumbersCommutative Property – interchange or switch the elements Example shows commutative property for addition: X + Y = Y + X Think of the elements as “commuting” from one location to another. “They get in …
Set-builder & Interval Notation
Set-builder & Interval NotationA set is a collection of unique elements. Elements in a set do not “repeat”.Methods of Describing Sets:Sets may be described in many ways: by roster, by set-builder notation, by interval notation, by graphing on a numb…
Multiplication and Division of Radicals
Multiplication and Division of Radicals(For this lesson, the term “radical” will refer only to “square root”.) When multiplying radicals, you must multiply the numbers OUTSIDE (O) the radicals AND then multiply the numbers INSIDE (I) the radicals.When d…
Graphing Functions and Examining Coefficients
Graphing Functions and Examining CoefficientsBehavior of Specific FunctionsLinear Functions:Linear functions are straight lines. Form being examined is y = mx + b. Equation Forms:Slope-Intercept Form: y = mx + b m = slope; b = y-interceptPoint-Slope For…
Solving Linear Inequalities
Solving Linear InequalitiesSolving linear inequalities is the same as solving linear equations with one very important exception…When you multiply or divide an inequality by a negative value, it changes the direction of the inequality. Basic Properties …
Dividing Powers
Dividing PowersRule: For all numbers x (not zero) and all integers m and n, “This simply means when you are dividing, and the bases are the same, you SUBTRACT the exponents.” (top exponent subtract bottom exponent)Consider: Observe this rule at work in…
Binary Operations
Binary OperationsA binary operation is simply a rule for combining two objects of a given type, to obtain another object of that type. You first learned of binary operations in elementary school. The objects you were using were numbers and the binary ope…