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.