$the quadratic formula$

#The quadratic formula how to#

Still, this raises the question of when a quadratic is easy to factor. This can make your calculations more error-prone, and it can take more time than an easy factor. The reason is that the quadratic formula involves both a radical and a fraction. If the quadratic is easy to factor, then you might want to skip the quadratic formula and just factor. If a quadratic is not easily factorable, then go ahead and use the quadratic formula.

When To Use The Quadratic Formula vs Factoring Let’s take a look at some scenarios where you might use methods other than the quadratic formula to solve a quadratic equation.

Just because you can always use the quadratic formula doesn’t mean you should always use it. However, the quadratic formula is one tool in your mathematical toolkit. Remember that the discriminant is the expression b 2 – 4ac (which is found under the radical in the numerator of the quadratic formula). 3.) Two Complex Solutions (Two Distinct Complex Conjugate Roots).2.) One Real Solution (One Repeated Real Root).1.) Two Real Solutions (Two Distinct Real Roots).When you use the quadratic formula, there are three basic cases: Of course, there are some situations when the solutions will be complex or imaginary. No matter what coefficients you have in the quadratic equation, the quadratic formula will always find a solution. There is no restriction on the values of the coefficients a, b, and c, except that a cannot be zero (otherwise, we would not have a quadratic in the first place – we would have a line). You can always use the quadratic formula to solve a quadratic equation. Can You Always Use The Quadratic Formula?

#The quadratic formula how to#

The ChiliMath website has an excellent write-up on how to derive the quadratic formula by completing the square. In fact, we complete the square for the standard form of the quadratic equation in order to derive the quadratic formula. The quadratic formula is a shortcut for the method of completing the square. ( If you are confused by the difference between a quadratic equation and the quadratic formula, this article will help).

ax 2 + bx + c = 0 (where a is not zero).

The quadratic formula gives the solution for the standard form of the quadratic equation

Problems that involve gravity (tracking the position of falling objects).

Finding roots of a quadratic equation (when it is difficult to factor).

Finding zeros of a parabola (finding the x-intercepts on the graph of a quadratic).

The quadratic formula is used in several different scenarios in math and physics, including:

We’ll also take a look at some examples to illustrate the idea. In this article, we’ll talk about when to use the quadratic formula. Of course, there are certain situations when factoring is easier than using the quadratic formula. In addition, the quadratic formula is useful in physics to deal with gravity and falling objects. You can also use the quadratic formula to find the roots of a quadratic equation if factoring is difficult. So, when do you use the quadratic formula? You can use the quadratic formula to find the zeros (x-intercepts) of a parabola. The quadratic formula is one method that helps you to solve these equations. Quadratic equations appear all the time in math, and you need to know how to solve them.