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Tips on Solving Quadratic Functions

by Karla Davisio (2020-05-22)

Being able to solve quadratic functions is an important skill to have in the field of algebra. Solving quadratic functions is the first step to plotting the problems that they represent in analytical geometry, for example. This graphical representation can then be used to find other pieces of information, such as the point of intersection of this parabola with another geometrical entity such as a straight line. Unfortunately, initially solving quadratic functions can be a somewhat demanding and time-consuming task, especially if you have not yet been introduced to the quadratic formula. This article will explore some of the various tips and tricks that you can stick to in order to solve quadratic functions correctly.

Learn Your Multiplication Tables
A solid foundation in arithmetic is an absolute must if you intend to solve quadratic functions. You need to be able to instantly tell what number multiplied by what other number gives a certain number. Additionally, you also need to know the combinations that arise when these two numbers are added to one another. This skill is the foundation for quadratic factoring which is necessary to solve quadratic functions correctly.

Learn to Factor
Factoring can be done in a variety of different ways. For example, if there are multiple terms, among one which there is a like term, you can take the greatest common factor between all of these like terms out of the equation. Additionally, you can also write my essay the quadratic expression as a product of two linear expressions. The middlemost number represents the sum of the first and last numbers in the two expressions linear expressions, whereas the last number in the quadratic expression represents their product.

Learn Perfect Squares
Being able to identify perfect squares is another essential skill to have when it comes to factoring quadratic expressions. In many cases, a cluttered expression can be represented as a certain linear expression that was raised to the power two. The expressions (X+Y)-squared and (X-Y)-squared are two examples of such perfect squares. You can usually tell a perfect square apart from another quadratic expression by the fact that its first term, and its last term are both squares.

Learn to Eliminate Extraneous Roots
Extraneous roots are solutions to your quadratic equation that seem likely, but are actually completely incorrect. Usually, these arise when you derive your quadratic expression by raising the expressions of a certain equations the power to on both sides. When you do such a thing in order to solve your equation, you may end up with values that deceptively turn up in factored form of your quadratic expression. When you arrive at these values, it is a good idea to plug them back into the initial equation in order to see if they balance out correctly. Otherwise, you can eliminate them as extraneous roots.

Learn the Quadratic Formula
The catch all that you can use to ensure that you solve quadratic functions correctly is the quadratic formula. The quadratic formula is an excellent formula that provides you with both answers to a certain quadratic expression directly without you having to intuitively use your knowledge of mathematics in order to arrive at the two linear expressions that represent quadratic equation in question. The only downside to this formula is that it is somewhat cumbersome, time-consuming, and difficult to memorize. Thus, you should only use the poverty formula as a last resort when regular factoring fails.

There are plenty of things that you can do in order to solve quadratic functions quickly and effectively. For example, you can increase upon your chances of correctly solving quadratic functions by having a firm foundation in arithmetic and being able to multiply and divide values quickly and accurately. It should also be within your capabilities to find the sums that give rise to certain numbers when multiplied by one another. When solving quadratic functions, we need to be especially careful not to end up with any extraneous roots; one best practice that you can do in order to ensure that this does not happen is the plug your solutions back into the initial equation in order to ensure that they check out.