I’m a little surprised how little is generally done to prepare students for the quadratic or linear equations when they have been in mathematics for a long time. Even as I am an instructor in an advanced undergraduate course on Calculus, for example, I find that few students are prepared to go through the process of creating an Inverse Problem Solver. Moreover, this seems to be overlooked in college-level mathematics courses.
The quadratic equation is used in physics and in chemistry to describe certain physical phenomena. It seems like a simple calculation problem but there are many variations to it. Often students will not understand why these variations exist so they cannot readily come up with a suitable and coherent answer.
Students can easily go through a quadratic worksheet and solve for x minus y. However, there are also different ways to construct the integral, and the student may want to work through a quadratic worksheet from various methods. For example, one way that you can construct the integral is from the simplest method known as the Method of Lemma.
You begin by dividing the xy-plane into two planes. On one plane there are a line and on the other line there is a point. Draw a line parallel to both points. Now, connect the point A to the origin.
The next step is to connect the point B to the point C. Then take the area of the line from A to B and subtract the area of the line from the point C. Then take the area of the line from B to C and subtract the area of the line from the point D. The result is an area of the line from point C to point D.
Lastly, take the difference between the two areas and divide by the first number (x – y). The result is the area of the line. Now, you have the integral. Another way to construct the integral is from two graphs.
The first thing that you do is draw a line on the xy-plane. Then, connect the point A to the origin. The second thing that you do is draw a line on the xy-plane that runs parallel to the original line. Then, connect the point B to the point C. The next thing that you do is draw a line that runs perpendicular to the original line from point C to point D.
The main reason that you do this is because it is possible to find the derivative of any function with respect to x and y and complex numbers. After a student has done the quadratic or linear equation in these ways, they can then proceed to the quadratic or linear equation in more complex ways.