Topic

SOLVING QUADRATIC EQUATIONS (Quadratic Formula Method)

Team member

RATHEESAN RASENTHIRAN

 Overview

This section is about solving quadratic equations. Quadratic equations are solved for the purpose of finding the x-intercepts involved, and to solve for x-values. In mathematics, a quadratic equation is a polynomial equation of the second degree. Students can expect questions in the general form of ax+bx + c = 0. Students must solve these types of standard questions using the quadratic formula, and also finding the nature of roots using the discriminant.  

Study Tips, Methods, and/or Advice

A quadratic function is a polynomial function of the form y = ax+bx + c, where a. If the quadratic function is set to be equal to zero, then the result is a quadratic equation.

               Remember

             y = ax+bx + c                 QUADRATIC FUNCTION

                0 = ax+bx + c                  QUADRATIC EQUATION

QUADRATIC EQUATION

We want to know for which values of x the equation is true to. If your function has a value on the right, you need to rearrange the equation so that it is in the form of ax+bx + c = 0.                    

                                                                          constant coefficient

                                   ax+bx + c = 0

                                                                          linear coefficient

                   quadratic coefficient

            5 METHODS OF SOLVING QUADRATIC EQUATIONS

(1)   Graphing

(2)    Factoring

                                                             (3) Algebra

                                                             (4) Completing the Square

                                                             (5) Quadratic Formula

In this section, we will only be exploring the Quadratic Formula method of solving Quadratic equations.

                   QUADRATIC FORMULA à x =

It is called the quadratic formula because it states the solution, providing a formula for computing the simplified answer(s) by using the values of the quadratic equation. To use it, you need to substitute your values into the equation in place of the letters, taking care not to miss the negative sign on the top row.

EXAMPLE- Solve for x.

                    y =                        

             Here a = 1, b= 5, c= 6                   

  Therefore, we get:

=        

=   =           OR         =

Note

The quadratic formula sometimes leads to a negative number under the square root sign. When this happens, the calculation cannot be completed using ordinary numbers (called real numbers). In this case, the relation has no real roots.

**Numbers such as are called imaginary numbers. They are not real numbers since the square root of a negative number does not exist in the set of real numbers. They are part of a larger set of numbers called complex numbers, which are important in advanced mathematics. When an equation has no real roots, it may have complex or non-real roots.

The value under the square root sign (), known as the “discriminant”, provides much information. The discriminant allows you to predict the nature of the roots.

You will get one of the three results:

            1.            2.            3.   

              2 real values for x         2 equal roots for x      Roots are complex, not real

EXAMPLE- Determine the nature of the previous question

                    y =                

             a = 1    b= 5     c= 6    

        Therefore, we get:            

                                    = 25 – 16

                                    =  9

      In this case, we’ll get two real and distinct roots since the discriminant is positive.      

Sample Questions and complete solutions

Extra Practice Questions and Answers

Self Reflection

Personal Reflection – Ratheesan Rasenthiran

Overall, I think this topic of solving quadratic equations using the quadratic formula is quite easy. To be honest, it is mighty easy. I was one of the last people to choose their topic for their assignment, and I barely had any options left. I forgot all about quadratic equations and formulas, so I thought this topic was going to be hard. After I reviewed me notes, I realized that I may have had the easiest topic amongst everyone in my class. Just just replacing its variables with values from the quadratic equation solves the quadratic formula. The replacements are given to us, directly from the equation. It doesn’t get easier than that. The only problem with the quadratic formula is that if you mess up with the signs and the calculations within the formula, it will lead you towards incorrect results. This could waste your time, when you have to go through all your work to find the error. Since there are 5 different methods of solving quadratic equations, I’m glad that I have the opportunity to use other options to come up with the correct values. I would rather use the algebraic method to find my answer. I feel most comfortable using that method.

    Over this semester, I have been able to learn quickly and understand the concepts of this course with great ease. I owe a lot of that to Ms. Demakopoulos. The way she teaches has made it easy for me to learn. Before coming to this class, I was scared that I would get a teacher that would not know how to teach, because I had Mr. Slemon for math 2 years of my high school career, and he really set the bar high. By the beginning of the Grade 11 math course, I knew Ms. Demakopoulos was going to be able to stand up to his standards, and be able to teach really well. I would take this opportunity to thank Ms. Demakopoulos for being my math teacher and it would be an honour, if I have her again in the future years.