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	Simplifying Fractions 3
	Factoring quadratics
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	Example 6
	Dividing Monomials
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	Simplification of Expressions Containing only Monomials
	Decimal Numbers
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	Percent Introduced
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	The Hyperbola
	Standard Form for the Equation of a Line
	Multiplication by 75
	Solving Quadratic Equations Using the Quadratic Formula
	Raising a Product to a Power
	Solving Equations with Log Terms on Each Side
	Monomial Factors
	Solving Inequalities with Fractions and Parentheses
	Division Property of Square and Cube Roots
	Multiplying Two Numbers Close to but less than 100
	Solving Absolute Value Inequalities
	Equations of Circles
	Percents and Decimals
	Integral Exponents
	Linear Equations - Positive and Negative Slopes
	Multiplying Radicals
	Factoring Special Quadratic Polynomials
	Simplifying Rational Expressions
	Adding and Subtracting Unlike Fractions
	Graphuing Linear Inequalities
	Linear Functions
	Solving Quadratic Equations by Using the Quadratic Formula
	Adding and Subtracting Polynomials
	Adding and Subtracting Functions
	Basic Algebraic Operations and Simplification
	Simplifying Complex Fractions
	Axis of Symmetry and Vertices
	Factoring Polynomials with Four Terms
	Evaluation of Simple Formulas
	Graphing Systems of Equations
	Scientific Notation
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	Horizontal and Vertical Lines
	Solving Equations by Factoring
	Solving Systems of Linear Inequalities
	Adding and Subtracting Rational Expressions with Different Denominators
	Adding and Subtracting Fractions
	Solving Linear Equations
	Simple Trinomials as Products of Binomials
	Solving Nonlinear Equations by Factoring
	Solving System of Equations
	Exponential Functions
	Computing the Area of Circles
	The Standard Form of a Quadratic Equation
	The Discriminant
	Dividing Monomials Using the Quotient Rule
	Squaring a Difference
	Changing the Sign of an Exponent
	Adding Fractions
	Powers of Radical Expressions
	Steps for Solving Linear Equations
	Quadratic Expressions Complete Squares
	Fractions 1
	Properties of Negative Exponents
	Factoring Perfect Square Trinomials
	Algebra
	Solving Quadratic Equations Using the Square Root Property
	Dividing Rational Expressions
	Quadratic Equations with Imaginary Solutions
	Factoring Trinomials Using Patterns

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The Standard Form of a Quadratic Equation

When we use mathematics to model real world situations, we sometimes use quadratic equations. Such equations are also called second degree equations, or equations of degree 2.

Definition â€” Quadratic Equation

A quadratic equation in one variable is an equation that can be written in the form ax² + bx +c = 0

where a, b, and c are real numbers and a ≠ 0.

This is called the standard form of a quadratic equation.

Note:

A quadratic equation must have a term of degree 2, such as x².

It cannot have a term of higher degree.

In the definition, notice that the terms on the left side of the equation are arranged in descending order by degree. The right side of the equation is zero.

We can also write a quadratic equation with 0 on the left side, like this: 0 = ax² + bx + c

Here are some examples of quadratic equations. To determine the values of a, b, and c, we first write the equation in standard form, ax² + bx + c = 0.

Non-standard form

x² - 3x = 28

5x² = -45

-3x² = -12x

Standard form

1x² - 3x - 28 = 0

5x² + 0x + 45 = 0

-3x² + 12x + 0 = 0

a = 1, b = -3, c= -28

a = 5, b = 0, c = 45

a = -3, b = 12, c = 0

The variable in a quadratic equation can be any letter, not just x.

For example: 3y² + 5y - 9 = 0 is a quadratic equation.

Example 1

For each of the following, if the equation is quadratic, write it in standard form and identify the values of a, b, and c.

a. 3x(x + 4) = 18

b. -6x² = 8 - 3x(2x + 1)

c. 0 = 7x²

Solution

Distribute 3x.

Subtract 18 from both sides.

This is a quadratic equation in standard form.

Here a = 3, b = 12, and c = -18.

3x(x + 4)

3x² + 12x

3x² + 12x - 18

= 18

= 0

Distribute -3x.

Add 6x² to both sides and rearrange terms.

Because the coefficient of the x²-term is 0, the equation is not a quadratic equation.

- 6x²

= 8 - 3x(2x + 1)

= 8 - 6x² - 3x

= 0x² - 3x + 8

= -3x + 8

Fill in the missing x-term and the missing constant term. This is a quadratic equation,

ax² + bx + c = 0, where a = 7, b = 0, and c = 0.

= 7x²

= 7x² + 0x + 0