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Absolute Values
Solving Two-Step Equations Algebraically
Multiplying Monomials
Factoring Trinomials
Solving Quadratic Equations
Power Functions and Transformations
Composition of Functions
Rational Inequalities
Equations of Lines
Graphing Logarithmic Functions
Elimination Using Multiplication
Multiplying Large Numbers
Multiplying by 11
Graphing Absolute Value Inequalities
The Discriminant
Reducing Numerical Fractions to Simplest Form
Addition of Algebraic Fractions
Graphing Inequalities in Two Variables
Adding and Subtracting Rational Expressions with Unlike Denominators
Multiplying Binomials
Graphing Linear Inequalities
Properties of Numbers and Definitions
Factoring Trinomials
Relatively Prime Numbers
Rotating a Hyperbola
Writing Algebraic Expressions
Quadratic and Power Inequalities
Solving Quadratic Equations by Completing the Square
BEDMAS & Fractions
Solving Absolute Value Equations
Writing Linear Equations in Slope-Intercept Form
Adding and Subtracting Rational Expressions with Different Denominators
Reducing Rational Expressions
Solving Absolute Value Equations
Equations of a Line - Slope-intercept form
Adding and Subtracting Rational Expressions with Unlike Denominators
Solving Equations with a Fractional Exponent
Simple Trinomials as Products of Binomials
Equivalent Fractions
Multiplying Polynomials
Graphing Equations in Three Variables
Properties of Exponents
Graphing Linear Inequalities
Solving Cubic Equations by Factoring
Adding and Subtracting Fractions
Multiplying Whole Numbers
Straight Lines
Solving Absolute Value Equations
Solving Nonlinear Equations
Factoring Polynomials by Finding the Greatest Common Factor
Algebraic Expressions Containing Radicals 1
Addition Property of Equality
Three special types of lines
Quadratic Inequalities That Cannot Be Factored
Adding and Subtracting Fractions
Coordinate System
Solving Equations
Factoring Polynomials
Solving Quadratic Equations
Multiplying Radical Expressions
Solving Quadratic Equations Using the Square Root Property
The Slope of a Line
Square Roots
Adding Polynomials
Arithmetic with Positive and Negative Numbers
Solving Equations
Powers and Roots of Complex Numbers
Adding, Subtracting and Finding Least Common Denominators
What the Factored Form of a Quadratic can tell you about the graph
Plotting a Point
Solving Equations with Variables on Each Side
Finding the GCF of a Set of Monomials
Completing the Square
Solving Equations with Radicals and Exponents
Solving Systems of Equations By Substitution
Adding and Subtracting Rational Expressions
Laws of Exponents and Dividing Monomials
Factoring Special Quadratic Polynomials
Solving Quadratic Equations by Completing the Square
Reducing Numerical Fractions to Simplest Form
Factoring Trinomials
Writing Decimals as Fractions
Using the Rules of Exponents
Evaluating the Quadratic Formula
Rationalizing the Denominator
Multiplication by 429
Writing Linear Equations in Point-Slope Form
Multiplying Radicals
Dividing Polynomials by Monomials
Factoring Trinomials
Introduction to Fractions
Square Roots
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Completing the Square

· Remember there are three forms a parabola equation can have

y = ax 2 + bx + c

y = (x + h)(x + k)

y = a(x - h) 2 + k

· The first one is the standard form. It provides us no details about the location of  the vertex. We can use the value of a to determine the direction the parabola opens.

· The 2nd is in factored form. The equation could have been presented in 1st form and was factored. If we set this equation to zero (so that y = 0) we can use it find the roots (where the parabola crosses the x axis)

· The 3rd form is the vertex form of the parabola. It tells us the direction of the parabola (the value of a ) and the values of h and k tells the location of the vertex.

· The goal of completing the square is to go from the 1st form to the 3rd form, or the vertex form.

o The process is very mechanical

§ Arrange in descending powers y = ax 2 + bx + c

§ Factor the equation so the first term (the one with the power) has a coefficient of one

y = (ax 2 + bx) + c

§ Now the process really begins. Take half the middle term and add and subtract the square of that number.

· By doing so you have set up the equation for easier manipulation. You can see that we haven’t changed the question, since we have added and subtracted the same number, we have in effect added zero.

§ We will now factor the first 3 terms, and move the 4th outside the brackets

§ This is the final product in a general form. It is to show you the

steps never change regardless of the coefficients!


word problems:

find the minimum product of 2 numbers whose difference is 8.

P = n(n-8) = n 2 - 8n à complete the square to get P = (n-4) 2 -16. the number will be 4 and the product will be 16.


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