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What is the Quadratic Formula?

The quadratic formula is considered one of the most potent tools in mathematics.


For most of the regions, the quadratic equation formula is introduced in the students in the first or second year of algebra classes. The quadratic formula is used to find the solutions of a polynomial equation of the form ax2 + bx + c = 0, where a, b and c are known values, “a” is referred to as the quadratic coefficient, “b” the linear coefficient, and “c” is always a constant. On the other hand, the value of "x" is unknown. The value of the quadratic coefficient or “a” cannot be set to be zero. If you want to set the value of the quadratic coefficient zero, then it must be in the linear form. The solution of quadratic equation formulas is also called roots. Term x-intercepts also used for them when the function on the left-hand side of the equation graphed, as they are “x” values that result in a “y” value of zero the definition of x-intercept. But keep in mind, a quadratic equation or a quadratic function set equal to a number, and the quadratic formula is not the same. The quadratic formula is always used to solve a quadratic equation set equal to zero.

Essential Points to Consider While Solving a Quadratic Equation

There are certain vital things that one can consider while solving a quadratic equation using the quadratic formula. But one of the essential points to remember when finding the roots of a quadratic equation using the quadratic formula is that you must first set the equation equal to zero. Otherwise, your “c” value will be off; however much you have left on the right-hand side value of the comparison, which will make your calculation of the roots incorrect. You can overcome this mistake by practicing.

Derivation of Quadratic Formula

As we discussed above, a quadratic equation is a polynomial equation of the form ax2 + bx + c = 0, where a, b and c are known values, “a” is referred to as the quadratic coefficient, “b” the linear coefficient, and “c” is always a constant. On the other hand, the value of x is an unknown. So, let’s consider this equation and find the quadratic formula to solve a quadratic equation.

  • ax2 + bx +c = 0
  • Multiply both sides by 4a,
  • 4ax2 + 4abx + 4ac = 0
  • Subtract 4ac from both sides,
  • 4ax2 + 4abx = -4ac
  • Add b2 to both sides,
  • 4a2x2 + 4abx + b2 = 0
  • Since
  • (m + n)2 = m2 + 2mn + n2
  • Complete the square on the left slide,
  • (2ax + b)2 = b2 – 4ac= D
  • Take square roots,
  • 2ax +b = ± √D
  • 2ax= -b ± √D
  • And divide by 2a, we get
  • x = −b ± √(b2 − 4ac) / 2a : Quadratic Formula

There are ways to solve a quadratic equation other than the quadratic formula. You can use factoring, completing the square or graphing methods to solve a quadratic equation too. A quadratic equation will have one or two roots (solutions to the equation). These roots can be real or complex (which means they contain the number “I”). A quadratic condition will have one root when the vertex of the parabola it speaks to lays on the x-pivot. While it will have one or two roots, it might have zero x-intercepts, as the roots, as noted, can be complicated (i.e., the parabola represented by the quadratic equation does not cross the x-axis). Here is a little trick to get more than you bargained for out of your quadratic formula calculations: While the solutions to a quadratic equation (yielded by the quadratic formula) are also the x-intercepts of the parabola represented by the quadratic equation (if the answers are real), they also can tell you the location of the parabola's vertex. How? Well, since a parabola is symmetrical, you know that the x coordinate of the vertex has to be halfway between the x coordinates of the two x-intercepts. Once you see the x coordinate of the vertex, finding the "y" coordinate is as easy as plugging that x coordinate into the quadratic function you started with (after all, your quadratic function is set up such that each x yields one y, so you just have to plug your x into the function to get its corresponding y value). Let’s have a graphical representation of the parabola of the quadratic equation below.

Quadratic Formula Calculator

Quadratic Formula Calculator “An A.I based Quadratic Formula Solver or Quadratic Calculator.”

There are many numbers to juggle and very little precisions when solving for the roots of a quadratic equation. So, it is advisable for you, even you are a master, to be very careful with your calculations if carrying them out by hand. But this can take a very long time to solve a quadratic equation. So here, our quadratic formula calculator plays the role of giving you the ability to solve as many quadratic equations as you want without any hassle. The quadratic calculator is one of the easiest to use quadratic formula calculator to solve any quadratic equation. You only need to put the value of known coefficients such as “a,” “b,” and “c” in respected boxes in our quadratic formula calculator and then click on the convert button. You will get your results or X1 or X2 values of a quadratic equation within a few seconds without any hassle and spending too much time because of our efficient and fast quadratic formula calculator. The “status” section on our quadratic formula calculator will let you know about the status of the quadratic equation, either it is solvable or not. Our quadratic formula calculator or quadratic solver, or you can say quadratic formula solver is not only easy to use but also absolutely free. So if you are looking for an amazingly fast quadratic formula calculator to solve your complex quadratic equations, then try our quadratic calculator. We are hopeful that you get what you are looking for in a quadratic formula calculator. Furthermore, our quadratic formula calculator gives you the freedom to use fractional coefficient values. If you want to know the real-world applications of a quadratic formula, then it is used to calculate areas, projectile trajectories, and speed, etc. 

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Amber Jha
2020-Feb-10
Good help