Quadratic equation

completing the square only works with quadratic functions, otherwise the equation will not be able to solve. An important rule to understand when deriving the quadratic formula by completing the square, is that the leading term must equal to “1”. On the other hand, if the leading term does not equal to “1”, one will have to factor the equation by dividing each term by the leading term. The quadratic equation must start as the following: 〖ax〗^2+bx+c=0. Next, the constant number is to be moved to the other side of the equation. Another important rule in math is that whenever a number is moved, the sign changes. In this case the constant “c” is positive, and later changed as “-c” when moved to the right side of the equation. As a result, it should look like the…

I think, overall, that my lesson went well. My lesson plan was focused on students building off their previous knowledge of solving quadratics to understand complex solutions of quadratics. For this lesson I started off by allowing students to solve a quadratic I had written on board. However the quadratic equation I had written on the board was the wrong equation so students got stuck when they tried to use the quadratic equation because they got a negative under the square root. From there, we…

The zeros are where the graph crosses the X axis. These zeros are also known as the solutions or the roots. The types of zeros that functions can have are rational zeros, irrational zeros, or complex zeros. Rational zeros are just the basic integers. Irrational zeros have radicals that can’t be removed. Complex zeros have imaginary numbers. Out of these 3 types of zeros, a quartic function can only have 4 rational/irrational zeros, 2 rational/irrational zeros and 2 complex zeros, or 4 complex…

Introduction I’m going to start this paper with introducing the history of Pascal’s Triangle, time ranging from 2nd century BC to 18th century AD. Among all the academic works by ancient mathematicians, I’m going to focus on Jiu Zhang Suan Shu [Nine Chapters on the Mathematical Art] composed by Chinese scholars around 2nd century BC-10th century AD. I will use the binomial expansions derived from Pascal’s triangle as an example and then illustrate the coefficients expansion in general. After…

In order to derive the Quadratic Formula by completing the square, it was important to verify that the quadratic equation was in standard form which is ax? + bx + c = 0. By using this correct form, I prevented myself from using the wrong values for a,b, or c which could result in an incorrect solution. I began by rewriting the equation by subtracting c to the other side which isolated ax? + bx. I divided the equation by a because it was multiplied on the squared term. In addition, I took the…

deduce the equation landing position of the ball thrown by the robotic arm stand. We must create the equations in terms of the radius, height, arm rotation speed, and release angle. The equations must be made with those variables because, those variables are what can change where the ball will land in the cup, and will make the equation more useful to the client. To make sure the equation will remain accurate we have to keep track of all the units throughout the process. Knowing that all…

were a way for professors around the world to teach their classes online for free. Like most others, my thoughts on online education mostly revolved around second-rate scams and suspicious for-profit institutions (I’m looking at you, DeVry). However, curiosity got ahold of me, and I quickly signed up for several courses. As it turned out, these courses were structured similarly to college classes; they consisted of weekly video lectures and a forum for collaboration between the tens…

M is the resultant internal bending moment calculated about the neutral axis of the cross section, y in this case is the thickness of the beam divided by two, and I is the moment of inertia of the cross-sectional area about the neutral axis [4]. The final equation is, Equation 5 is utilized to calculate the deflection δ of the cantilevered beam at x = L when a load is applied at a point. Since we would not applying a specific load but knowing the displacement we solved this equation for P. There…

This is where they began to know a little about each other and how they all got in to Princeton. After meeting and taking to one another Nash starts to walk to his dorm. As John got to his dorm, he looks around and decides to move his desk to the window. Then a guy name Charles Herman walks into the dorm and introduce himself as his roommate. Charles came in the dorm like he was some kind of a drunk person but he was not drunk. After that, John started to write mathematical equation on his…

This method also is called quadratic exponential (QE method), which is be considered as one of the best algorithms for simulating from the Heston model. However, this method relies on huge time steps(Tse & Wan 2013). To solve this problem, Tse and Wan present a model with Inverse Gaussian approximation and IPZ scheme, which can reduce the number of time steps needed for pursuing same accurate as QE method. Recently, Begin et al raise a new method for sampling, which can imply model parameters of…