Quadratic Equation Calculator with Definition, Example & Worksheet

Mathematics may not teach us how to add love or how to minus to hate, but it gives us a reason to hope that “Every Problem has a Solution”

–Anonymous

Hi everyone, our today’s topic is the quadratic equation. I know most of the visitors do not like mathematics and do understand the concept behind these equations. As the above mean that in mathematics, it gives us hope that every problem has a solution. Similarly, you should not lose hope and feel like that mathematics is not your cup of tea. I think mathematics is very to understand you just need a little bit of concentration and understating of the concepts. And this understanding comes when you co-relate the things or concepts of mathematics with real life. When you are able to relate mathematics to real-world examples then you will find that mathematics is very simple and easy to understand. You just need to understand the concept no need to remember proper solutions to same questions which lie under same topic or concept.

Quadratic Formula Definition

Here, in the article, I will discuss quadratic equations. Quadratic equation’s definition, examples, steps, formula, problems etc is discussed here. And all the details that are required to clarify the concept of quadratic equation to you.

So, let’s begin with the definition of quadratic formula:

Ax2 + Bx + C = 0

This is the quadratic equation for which the quadratic formula is implemented on. The quadratic equation consists of x component power of 2. There can be signs of +/-. To find the values of a, b, or c and this equation is solved with the help of quadratic formula.

Quadratic formula is:

Here, in this formula first we solve the that is the discriminant formula.  From this formula firstly it is used to check the types of coefficients like whether the coefficient consists of the positive sign, both values are equal or not or coefficient is of the negative sign. After getting discriminant value, quadratic formula is applied on the equation. Discriminant also helps to check the concept whether the roots are of real numbers or imaginary numbers. If they are of real number only then find out the roots otherwise you can leave this sum after finding discriminant.

Quadratic Formula Examples

To understand the concept of the Quadratic equation or formula we can take an example. Probably this example can help you in knowing that how the quadratic equations are solved with the help of quadratic formula. Quadratic equation can be used to solve the GRAPHS, REAL LIFE PROBLEMS, FINDING COFFICIENTS, and MIISING VALUE IN THE EQUATION etc.

Let’s try to solve this equation which I have mentioned in the below image.

Here, the numbers are the values of a, b, and c. You just need to put the values of these in the quadratic formula.

To solve this equation you need to have good grasp on the calculations. You must have needed to have strong knowledge of the solving squares and square-root. Only then you can solve this kind of equations easily with the less passage of time.

If you find difficult to solve this equation you can partition this equation in to two parts. Like fist you just solve the discriminent and then you just only need to write the value of the discriminant in the square-root part. You do not need to solve the whole equation at once. In some equations, the values of x may be equal in that case the discriminant value comes out to be ZERO. This is case in which you can solve the quadratic equation within the very less time span. So, solving discriminant first can help you to know what kind of answer you are going to get after solving the quadratic equation.

Quadratic Formula Calculator

If you have got some assignment to solve the quadratic equations and you are not aware whether the sums solved by you are correct or not then you can take help of quadratic formula calculator. Yes, you read correctly, there are online quadratic formula calculators available, you just need to put the values of and you can find out the coefficients.

These quadratic formula calculators to cross check your answers. This can help to build your confidence in solving quadratic equations.  And if you are getting wrong answers then you can find out the description that on which step you are doing wrong calculation. As to get the right answer in the quadratic equation you just need to be good in calculations. There is no chance of wrong calculation. If you did any wrong minor calculation whether in case of SIGNS, you will get garbage value or wrong answer. So, to make sure all the aspects you can take help of quadratic formula calculator to find the accuracy of your interpreted answer and calculator output.

Quadratic Formula Problems

Now, I have discussed a lot about quadratic formula, but did not discuss about the problems of the quadratic formula. So, in this sub section let’s discuss about the problems of the quadratic formula, so that quadratic formula can more easily be understood by you.

As I mentioned above quadratic formula can be used to solve the real life problems. When we correlate the problems with real life world problems then we can easily get to know about the concept and understand the things for long time period with the clearance of thoughts. So, you can also do the same. Try to solve the real life problems with the help of quadratic formula. Quadratic formula is normally used to solve the parabola equation. Like to calculate the time of the ball in the air when you through the ball. As the ball did not go straight and comes back straight. The ball covers parabola shape. Similarly the dolphin jumps example I have stated in the image, can be solved by the quadratic formula. Try to understand the problem I have stated in the image.

 

Quadratic Formula Steps

To solve the quadratic equation directly with the quadratic formula can be little bit difficult for the beginners. So, it is not necessary to put all the values at once and solve the formula. It can also lead you to the wrong calculation or ultimately wrong answer. So, you can solve this quadratic equation with the help of steps. You just need to solve these steps and you will ultimately get the answer. These steps also help you to understand the quadratic formula concept as well.

Let’s continue with the discussion of the steps below:

  • Firstly, you need to indentify the values of the constants. And the equation must be equal to the zero. So, if there is any constant value on the right side move the value to the left side where all other coefficient values are and also do not forget to change the sign of the value when you are shifting its side.
  • Secondly, find out the discriminent to check which kind of roots will come after the interpretation of whole the sum.
  • Now, put values of the constants in the quadratic formula, try to solve the equation in an easy way. As you have solved the discriminent at second step. You can directly write its value in the square-root portion.
  • In the end, you get the answer of the quadratic equation.

See, by solving mathematics problems in steps it becomes easy to understand and solve. So, you can follow these steps to solve the equation and to get the accurate answers as well.

What is the Quadratic Formula used for

We have discussed all the concept of quadratic formula and how to implement it or solve it. Now, the question arises that what is the quadratic formula used for?  Well, you will get the answer of this question also, in this article. I do not want you to leave you in any kind of doubt. So, the answer I have discussed a little bit in the above section also. The quadratic formula is used to solve the real life problems as well along with the solving mathematical equations, graphs, finding the solution of the quadratic equations like the quadratic equations can have more than one solution, unique solution or no solution also. So, to find out all such kind of problems which are expressed in the form of quadratic equation you can take help of quadratic formula is solve these problems. In the real life problems to find velocity, the initial point, final point, and all time interval when the particular thing is in the air when it is passed from one place to another. To find all these concepts the quadratic formula helps a lot.

Quadratic Formula Worksheet

You want to have good grasp on the quadratic formula then you can take help of quadratic formula worksheet. Now, you will again raise the question that from where you can get worksheet for the quadratic equations and formula than there is the large variety of the worksheets available on the internet. You can choose any of them from the easy level to the difficult one to solve the quadratic problems and can make your practice. There is a large number of collections of the worksheets available online. You just need to save this worksheet or you can solve these worksheets online as well. Once you understand the concept and you think you have become quite good in the quadratic formula then you can solve this worksheet on the quadratic formula along with timer option as well. The technology has developed a lot. Now, you do not need to go outside and purchase the worksheet to practice. You can get all the stuff here on the internet without spending money.  These worksheets are also available in the form of doc file or PDF format as well. So, you can download these files and can practice on these worksheets.

Roots of Quadratic Equation Calculator

The values of x we get after solving the quadratic equation is considered as the roots of the quadratic equation. Now, when we find out the discriminant we get to know about the concept that whether the roots are some or different and also these roots of the Quadratic equation are real numbers or imaginary numbers. If they are of imaginary numbers then that equation will have no solution. The roots of the quadratic equation in case of graphs are interpreted as x-axis and y-axis. And plot the values of the roots with respect to these vertices.  These values of x can be same as well. If the value comes out to be same then it forms a straight line on the graph with the conclusion of the unique solution.

 

Some mathematicians also used the concept of “sum of the roots and product of the roots” That is another simple method to find out the roots. In this method the roots values are finding out by splitting the value by checking the product of the roots values should be equal to the mid value and the sum of the roots should e equal to the extreme values. This is a very easy way to find out the values of the roots but for this you need to be aware of signs as well and need to be good hands on the calculation.

Quadratic Root Calculator

There is quadratic root calculator as well. You can use this calculator to find out the root values of the quadratic equation. These values can be solved by using the normal scientific calculator. And there is the option of online quadratic root calculator as well. You can choose any of them to solve these quadratic equations and to find the roots of the quadratic equations. If you know the formula or understand it well but not able to get the correct answer because you are not good in calculations then you can take help of these quadratic root calculators to find out the correct answer.

This is all about the QUADRATIC EQUATION. Hope, now you all get to know about the concepts of the quadratic equation and its formula. And how you can solve these quadratic equations easily and practice it as well. You just need to give some attention on the sums and you can easily find out the solution to the problems. Try to solve the quadratic problems because with the help of practice you will understand the concept more clearly. Once you start practising you will find out that quadratic equation is one the easiest topic of the mathematics.

 

Thank you