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.

Math Homework Help - How to Easily Identify and Solve Quadratic Equations

One of the most common questions that a student asks his or her algebra tutor when seeking math homework help concerns finding math solutions for problems involving quadratic equations. Before attempting to solve any equation, the algebra tutor should aid the student in identifying this type of equation. It can easily be identified by the highest power of the variable x, which should be equal to two. When math solutions require the student to solve a quadratic equation, the algebra tutor should focus on how to solve the equation for the value(s) of x when y is set equal to zero. In other words, the student should solve for the x-intercept(s). The x-intercept(s) are the point(s) at which the graph of the quadratic equation cross(es) the x-axis. Alternatively, the student may be asked to find the zeros or the roots of the quadratic equation, which are identical to solving for the x-intercepts! There are several different ways in which the student can solve this type of equation. Firstly though, y should be set equal to zero. Once this is accomplished, the equation can be solved using either graphing, factoring, or using the quadratic equation.

When providing math homework help, the algebra tutor should highlight that the least accurate method of solving the equation involves graphing the equation and noting where the graph crosses the x-axis. These points are referred to as the x-intercepts as mentioned before. Note that there may be either zero, one, or two x-intercepts. The math solutions for this type of problem are usually not listed as points, but rather as values of x. This method may potentially yield inaccurate solutions since it involves reading values off of a graph that may not have been drawn with complete precision by the student. In order to correct this problem, the student may also use a graphing calculator to check his or her math solutions.

Factoring is another, more exact method that can be used by a student seeking math homework help to solve a quadratic equation. From the start, the algebra tutor should emphasize that not all quadratic equations are factorable. For that reason, it is always a good idea for the student to as well be familiar with using the quadratic formula which will be discussed shortly. Factoring can be useful since it is quick and can easily be checked by plugging the solutions back into the original quadratic equation.

The last method to be discussed is the quadratic formula. This method is foolproof in that the student does not necessarily need to know how to factor the original quadratic equation. Also, this method allows the student to solve for x-intercepts that are not necessary whole numbers. In other words, in terms of math homework help geared toward the student, the quadratic equation can be used to solve for radical, irrational, or even imaginary solutions! The algebra tutor should as well help the student realize that the quadratic formula can only be used to find solutions when the original equation is in general (or standard) form. This means that the quadratic equation cannot be in vertex form. If this is the case, the quadratic equation can easily be converted to general form so the quadratic formula can be used. In the quadratic formula, a represents the coefficient of the term with the x-squared term, b represents the linear coefficient, and c represents the constant term (the term with no variable multiplied onto it). Once these are identified, the quadratic formula can easily be used to find math solutions for a variety of different problems involving equations.

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Math Homework Help - How to Easily Identify and Solve Quadratic Equations

One of the most common questions that a student asks his or her algebra tutor when seeking math homework help concerns finding math solutions for problems involving quadratic equations. Before attempting to solve any equation, the algebra tutor should aid the student in identifying this type of equation. It can easily be identified by the highest power of the variable x, which should be equal to two. When math solutions require the student to solve a quadratic equation, the algebra tutor should focus on how to solve the equation for the value(s) of x when y is set equal to zero. In other words, the student should solve for the x-intercept(s). The x-intercept(s) are the point(s) at which the graph of the quadratic equation cross(es) the x-axis. Alternatively, the student may be asked to find the zeros or the roots of the quadratic equation, which are identical to solving for the x-intercepts! There are several different ways in which the student can solve this type of equation. Firstly though, y should be set equal to zero. Once this is accomplished, the equation can be solved using either graphing, factoring, or using the quadratic equation.

When providing math homework help, the algebra tutor should highlight that the least accurate method of solving the equation involves graphing the equation and noting where the graph crosses the x-axis. These points are referred to as the x-intercepts as mentioned before. Note that there may be either zero, one, or two x-intercepts. The math solutions for this type of problem are usually not listed as points, but rather as values of x. This method may potentially yield inaccurate solutions since it involves reading values off of a graph that may not have been drawn with complete precision by the student. In order to correct this problem, the student may also use a graphing calculator to check his or her math solutions.

Factoring is another, more exact method that can be used by a student seeking math homework help to solve a quadratic equation. From the start, the algebra tutor should emphasize that not all quadratic equations are factorable. For that reason, it is always a good idea for the student to as well be familiar with using the quadratic formula which will be discussed shortly. Factoring can be useful since it is quick and can easily be checked by plugging the solutions back into the original quadratic equation.

The last method to be discussed is the quadratic formula. This method is foolproof in that the student does not necessarily need to know how to factor the original quadratic equation. Also, this method allows the student to solve for x-intercepts that are not necessary whole numbers. In other words, in terms of math homework help geared toward the student, the quadratic equation can be used to solve for radical, irrational, or even imaginary solutions! The algebra tutor should as well help the student realize that the quadratic formula can only be used to find solutions when the original equation is in general (or standard) form. This means that the quadratic equation cannot be in vertex form. If this is the case, the quadratic equation can easily be converted to general form so the quadratic formula can be used. In the quadratic formula, a represents the coefficient of the term with the x-squared term, b represents the linear coefficient, and c represents the constant term (the term with no variable multiplied onto it). Once these are identified, the quadratic formula can easily be used to find math solutions for a variety of different problems involving equations.

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.