Free Algebra
Tutorials!
 
Home
Point
Arithmetic Operations with Numerical Fractions
Multiplying a Polynomial by a Monomial
Solving Linear Equation
Solving Linear Equations
Solving Inequalities
Solving Compound Inequalities
Solving Systems of Equations Using Substitution
Simplifying Fractions 3
Factoring quadratics
Special Products
Writing Fractions as Percents
Using Patterns to Multiply Two Binomials
Adding and Subtracting Fractions
Solving Linear Inequalities
Adding Fractions
Solving Systems of Equations -
Exponential Functions
Integer Exponents
Example 6
Dividing Monomials
Multiplication can Increase or Decrease a Number
Graphing Horizontal Lines
Simplification of Expressions Containing only Monomials
Decimal Numbers
Negative Numbers
Factoring
Subtracting Polynomials
Adding and Subtracting Fractions
Powers of i
Multiplying and Dividing Fractions
Simplifying Complex Fractions
Finding the Coordinates of a Point
Fractions and Decimals
Rational Expressions
Solving Equations by Factoring
Slope of a Line
Percent Introduced
Reducing Rational Expressions to Lowest Terms
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
Lines and Equations
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
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


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 — 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

a.  

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

= 18

= 0

b.  

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

- 6x2

0

0

= 8 - 3x(2x + 1)

= 8 - 6x2 - 3x

= 0x2 - 3x + 8

= -3x + 8

c.  

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.

0

0

= 7x2

= 7x2 + 0x + 0

All Right Reserved. Copyright 2005-2017