	Algebra Tutorials!

Thursday 21st of November



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	Calculations with Negative Numbers
	Solving Linear Equations
	Systems of Linear Equations
	Solving Linear Equations Graphically
	Algebra Expressions
	Evaluating Expressions and Solving Equations
	Fraction rules
	Factoring Quadratic Trinomials
	Multiplying and Dividing Fractions
	Dividing Decimals by Whole Numbers
	Adding and Subtracting Radicals
	Subtracting Fractions
	Factoring Polynomials by Grouping
	Slopes of Perpendicular Lines
	Linear Equations
	Roots - Radicals 1
	Graph of a Line
	Sum of the Roots of a Quadratic
	Writing Linear Equations Using Slope and Point
	Factoring Trinomials with Leading Coefficient 1
	Writing Linear Equations Using Slope and Point
	Simplifying Expressions with Negative Exponents
	Solving Equations 3
	Solving Quadratic Equations
	Parent and Family Graphs
	Collecting Like Terms
	nth Roots
	Power of a Quotient Property of Exponents
	Adding and Subtracting Fractions
	Percents
	Solving Linear Systems of Equations by Elimination
	The Quadratic Formula
	Fractions and Mixed Numbers
	Solving Rational Equations
	Multiplying Special Binomials
	Rounding Numbers
	Factoring by Grouping
	Polar Form of a Complex Number
	Solving Quadratic Equations
	Simplifying Complex Fractions
	Algebra
	Common Logs
	Operations on Signed Numbers
	Multiplying Fractions in General
	Dividing Polynomials
	Polynomials
	Higher Degrees and Variable Exponents
	Solving Quadratic Inequalities with a Sign Graph
	Writing a Rational Expression in Lowest Terms
	Solving Quadratic Inequalities with a Sign Graph
	Solving Linear Equations
	The Square of a Binomial
	Properties of Negative Exponents
	Inverse Functions
	fractions
	Rotating an Ellipse
	Multiplying Numbers
	Linear Equations
	Solving Equations with One Log Term
	Combining Operations
	The Ellipse
	Straight Lines
	Graphing Inequalities in Two Variables
	Solving Trigonometric Equations
	Adding and Subtracting Fractions
	Simple Trinomials as Products of Binomials
	Ratios and Proportions
	Solving Equations
	Multiplying and Dividing Fractions 2
	Rational Numbers
	Difference of Two Squares
	Factoring Polynomials by Grouping
	Solving Equations That Contain Rational Expressions
	Solving Quadratic Equations
	Dividing and Subtracting Rational Expressions
	Square Roots and Real Numbers
	Order of Operations
	Solving Nonlinear Equations by Substitution
	The Distance and Midpoint Formulas
	Linear Equations
	Graphing Using x- and y- Intercepts
	Properties of Exponents
	Solving Quadratic Equations
	Solving One-Step Equations Using Algebra
	Relatively Prime Numbers
	Solving a Quadratic Inequality with Two Solutions
	Quadratics
	Operations on Radicals
	Factoring a Difference of Two Squares
	Straight Lines
	Solving Quadratic Equations by Factoring
	Graphing Logarithmic Functions
	Simplifying Expressions Involving Variables
	Adding Integers
	Decimals
	Factoring Completely General Quadratic Trinomials
	Using Patterns to Multiply Two Binomials
	Adding and Subtracting Rational Expressions With Unlike Denominators
	Rational Exponents
	Horizontal and Vertical Lines

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Solving Quadratic Equations

Quadratic Equation in One Variable: ax² + bx + c = 0, where a, b and c are real numbers with a ≠ 0. We will solve these equations by several methods.

I. Solving Quadratic Equations by Factoring

The Zero Product Property: ab = 0 if and only if either a = 0 or b = 0 or both a and b equal zero.

II. Graphical Solution

Once the equation is written in the form ax² + bx + c = 0, we can graph the left side as y₁ and find the x- intercepts. These x-intercepts or zeros of the function are the solutions to the quadratic equation ax² + bx + c = 0.

III. Square Root Property

The solution set of x² = k is:

IV. Using the Quadratic Formula to Solve Quadratic Equations

If ax² + bx + c = 0, a ≠ 0, then:

b² - 4ac is called the discriminant of the quadratic equation.

DISCRIMINANT AND ROOTS

If the discriminant is:	Then the equation has:
Positive	Two real solutions
Zero	One real solution
Negative	No real solutions