Quadratic Equations - An Introduction

Quadratic equations are the algebra topic taught to grade ten or eleven students. The word quadratic means, degree two in mathematics. Therefore any equation in degree two is called a quadratic equation. The form of standard quadratic equation is written as given below:

ax² + bx + c = 0

Where, "a", "b" and "c" are the real numbers and "a" can't be zero because in that case the quadratic term "ax²" becomes zero and the equation itself lose its identity and change to linear equation (degree one) which can be written as "bx + c = 0".

Some examples of quadratic equations are given below to make their identity more clear.

1. 3x² + 2x + 5 = 0

2. - x² + 3x - 9 = 0

3. x² + 1 = 0

4. - 9x² - 6x - 8 = 0

5. 4y² + 9 = 3y

Keep in mind that any letter can be used as a variable in the equations as I used "x" and "y" in the examples above.

In standard form these equations have three terms; first term in degree two called the quadratic term, second term in degree one called the linear term and third term is a constant number as shown in above examples.

Look at example # 3, there are only two terms in the equation. The term with degree one (linear term) is missing because the coefficient for this term is zero. This example can be written in standard form as shown below:

x² + 0x + 1 = 0

Now you have understood the way to write quadratic equations, the next step is to know about solving these equations. There are many ways to solve, such as solve by graphing, factor method, square root method, completing the square method and last but not least the formula method to solve quadratic equations.

To solve these equations using factoring method basic knowledge of factoring polynomials is required. You can read my articles about factoring polynomials for deeper knowledge about the topic.

To use formula to solve these equations, students should be very confident in radicals and they specially should have good knowledge of square roots. There is a special character used in formula called discriminate and is denoted by "D". The value of "D" is calculated by using the following formula:

D = b² - 4ac

Or in other words, linear coefficient "b" squared minus 4 times quadratic coefficient "a" times the constant term "c".

These equations if plotted on the graph, make a special cup shaped curve called parabola. There is a separate unit in grade eleven or twelve text books to study about parabolas.

There are many applications of these equations in higher algebra and to solve equations in higher degrees.

For more math resources and math worksheets my site can be visited or click for free 2nd grade math worksheets, for your kids in 2nd grade.