How Quadratic Equation Calculator Works

The quadratic equation calculator uses the quadratic formula in order to find the solution for the quadratic equation. The calculator can solve the quadratic equation if you type a simple type of the formula such as A, b, and C and then to hit the solve button.

Some calculator will show how the formula was used, but when you use the graphing calculator, you will solve the quadratic equation even with these that have the imaginary solution.

Quadratic Equation
Quadratic Equation

The calculator to solve the quadratic equation will help you to solve equation through completing the square and by the use of the quadratic formula. The calculator can write down the complete solution step by step.

With the calculators, you will not have to worry that there is something you do not understand. You will be taken to step by step in the learning process.  The algebra worksheet is the best way that you may hone the math skills and to practice if you have a math test.  You will not only learn about a possible solution but also get some tips.

The quadratic equation calculators are here to help you when you get stuck with a problem, and you are not able to figure it out. The calculator can help to solve the equation, and it gives details on how the problem was solved and how the answer was reached.   There are different online calculators online, and they work differently.  Some calculator can solve the problem through factoring, through completion of the square root or answering of the algebra questions.  You may find the graphing calculator, and they plot the equations. The calculators do use the technology, and it allows the plotted graphs to use up to 360 degrees. They provide a well-rounded understanding of the problems.

You can also find the algebra solvers on different websites. They are like the algebra calculator, but they are the software that offers the answers even on the tough equation.  What you will need to do is entering algebra problem, and then the software is going to do what it is left. The great algebra tool may help in providing the tutor whenever the student needs him, and it helps to reduce the costs with the long hours which come with paying the tutor.

If you want to find these calculators, you will only have to enter the name of the calculator you want in Google search. You will get some different calculators, and it is up to you to choose the one you like most.

The calculator helps the students who think that quadratic equations are a nightmare. When the students start to use the calculator and to keep up with their guides, then they will start to solve the problems on their own.

The calculator will put the method into chunks so that the students can learn about them much easily. The quadratic formula can be a mouthful but when it is divided into chunks, it will be manageable. When students see such method, they will realize that they will also use the same methods to other areas of the studies.

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What are a Quadratic Formula Calculator and its Standard Equation?

In elementary algebra, there are various ways of solving a quadratic equation such as completing the square, graphing or factoring. However and whenever you seek for a way to solve these equations the best way which comes to your mind is the Quadratic formula calculator. That is a one-step solution for all kind of quadratic equations. It is one of the simpler, easiest and convenient ways of solving equations. After reading this article, you will become able to identify a quadratic equation. You will learn how to place a quadratic equation into a standard form along with learning the alternative ways to derive a quadratic equation general formula.

Quadratic Formula
Quadratic Formula

A quadratic formula calculator in general terms could be called as a polynomial equation which contains the second degree and no higher degrees of a variable. The standard form of a quadratic equation is –

mx² + nx + k = 0

In this equation, the value of x is always unknown. m, n, and k are constant in which they should be equal to 0 or contains some negative and positive values. On the way to verify whether the quadratic formula is satisfying a quadratic equation or not, you have to insert the former one into the latter. This is known as parameterization. After this, the general quadratic formula is converted into

Math
Math

 

 

known as radical.

All the quadratic equations can be inserted in a standard form. And any equation which can be put into a standard form and can be solved by a quadratic formula solver represents a quadratic equation. The solution of any equation is sometimes known as the root of an equation.

There are various methods for deriving the quadratic formula. Some of these may either be simpler than completing the square method however the method represents interesting applications of the different algebraic techniques. It offers a different view of the field of mathematics.

How the general quadratic formula calculator is derived?

mx² + nx + k = 0

4m²x² + 4mnx + 4mk = 0

4m²x² + 4mnx = -4mk

4m²x² + 4mnx + n² = n² – 4mk

(2mx + n)² = n² – 4mk

equation
equation

 

 

 

 

This is an ancient way of determining the quadratic formula which was known to the people around years ago. When it is compared with other ways of deriving the standard formula, this way of solving and determining the formula is quite simpler. The benefits of this formula derivation are-

  • Simple to solve and is less complicated
  • Less computation of literal coefficients
  • It does not involve fractions until the very last steps.
  • Use of simple math with simple expressions
  • The central theme of algebra is to solve the equations

However solving these equations is not easy for everyone. A lot of times people find a problem get stuck into a particular quadratic equation and do not find the way to solve it. The basic command over mathematics is a must to solve such equations. However, there are various sites which are now offering the services of instantly solving the equations. One such site is the Quick Math which allows you to put down your equation in the available dialogue box to provide the quadratic formula calculator. The whole solution can be displayed along with the answer. It makes your math problems easier and explains the alternative ways to solve an equation.

When Quadratic Formula is Used

With elementary algebra, quadratic formula is used for the solution of a quadratic equation. You can find many ways that you can use to solve this problem without using the quadratic formula like graphing, completion of the square or factoring while using the quadratic formula maybe most convenient method. The quadratic equation looks like ax2+bx+c=0.  With this equation, x stands for unknown but a, b, with C should be constant, and A should not be zero. Someone may verify that the quadratic formula does satisfy quadratic equation through inserting the first number in the last number.

quadratic formula
quadratic formula

The solution found with the quadratic formula is known as the root for a quadratic equation.  In geometry, such roots can represent the value of x which is the parabola given will cross at the axis of X. The formula can yield zero of different parabola while quadratic formula can give axis to the symmetry of a parabola. This is normally used in order to determine the number of the zero which the quadratic equation does have.

The formula may get derived from the simple application with a technique application needed to complete a square. This is why; a derivation can be sometime left like the exercise of the students who wish to experience the rediscovery of the formula.

A quadratic equation can be in the form to complete a square when it is applied. You may add the constant on the two sides of an equation like the left-hand side which become the complete square.  The terms should be rearranged at a right-hand side so that we can obtain the common denominator. When the square had been completed, then the square root of the two sides have to be found and then isolating the x to get the quadratic formula.

The solution of a quadratic equation can be gotten by using different alternatives of the derivation with the minor differences, and this is through manipulating a. Some of the old sources may use the alternative of parameterization for the equation by using b with a magnitude of the half of a common number.  Even if the results can be different from the first solution, however, they are also equivalent.

Without the need to go in the parabolas like the geometrical objects of the cone, the parabola will be the curve which is being described as the second degree of the polynomial.

The early method to solve the quadratic equation was done in the geometry.   The Babylonian cuneiform tablet had the problems that are reducible in solving a quadratic equation. Egyptian Berlin Papyrus that dated back in the middle kingdom had some solution for a two-term equation.   In Greek, the mathematician Euclid was using the geometric method in order to solve the quadratic equation in the Elements Book 2.  The laws of the quadratic equation do appear in Nine Chapters on Mathematical Art circa from China. A Greek mathematician Diophantus in the work he did on the arthmetica, he solved some quadratic equations which are recognizable to the algebraic done by Euclid. The solution he used was able to give one root, regardless if positive roots were used.

How to Solve Equations using Quadratic Formula Calculator

Quadratic formula is the best and the easiest way of solving quadratic equations. Most mathematicians believe that this formula can solve even the complex quadratic equation you can think of. Then there is a quadratic formula calculator that uses the quadratic formula to solve equations. First of all a quadratic formula looks like the one below Math

Where x is the variable being solved, a, b and c being the numerical coefficients of the quadratic equation that you may come across. They literally represent any number that you can think of. The values of a, b and c could be 6, 11, and 28.

Learning the calculator through examples

If you do not know how to use the above formula, sit back and relax. But be very attentive. There is a website that you can use to learn these things. It is quickmath.com; the best online math tutoring site that anyone can access for free.

Let me show you how the site uses examples to solve quadratic equations using the quadratic formula calculator.

Example 1

Given an equation like this,  Math

It can be solved this way;

Math

Here, a equals to 10, b equals to -7, and c equals to -23

Therefore, we will get  Math

 

The final result will be Math

 

X= 1.8575 or

X=1.1575

The two answers should give you the same results. You can proof it by substituting x in the equation using any of its value we obtained here.

Example 2

Let us take a look at another example of a quadratic equation and try to solve it using the quadratic formula calculator. Remember, you can get to learn all these from http://www.quickmath.com.

An equation could be in the form of words. So, you will first have to deduce it there and form a quadratic equation then try to solve it.

Question: Solve for the value of x .if three times x squared plus two x minus eight equals to 10.

Okay, this is not a good example but was just trying to illustrate how you may come across such equations.

Forming an equation will be like Math

Using the quadratic formula of  Math

The equation will need to be simplified further since we still have some like terms that have not been grouped together. The final equation should be; Math

Therefore, an equals to 3, b equals to 2 and value of c will be -18

Math

Math

The values of x will be -2.805 and 2.14

You can use these values to ascertain that they are correct. If you did not get the above values for x, then you may have skipped some steps, and therefore the best thing you can do is to retrace your steps till the place you got lost. From there, you can start following the steps again. The good thing is that they are pretty straight forward steps.

Make sure you practice doing this regularly until you master it. Once that happens, nothing quadratic will prevent you from passing that math exam you are about to sit for.