Ray Tools: Quadratic Equations
Understanding quadratic equations (equations with square terms) can be daunting but this program simplifies understanding. Both from an educational standpoint where the student needs to understand factors and roots or from an engineering standpoint where the user needs to understand the relationship between distance, acceleration and time this program solves equations in a user friendly environment. Both a help file and glossary of terms have been included to simplify understanding. The equation takes the form of “Y = aX^2 + bX + c “ or “Y = (f1X +f2) * (f3X + f4) = 0” where the program allows factoring for the calculation of roots as well as defining and changing a, b and c coefficients to solve the quadratic equation {roots = (-b +/- sqrt(b^2-4*a*c))2a } for roots. Roots exist where the curve crosses or intersects the X axis meaning the points where Y = 0. In the conventional sense one sets up the factors and then solves for the roots. This program sets up the form and allows one to adjust the factors until the equation results in what is expected. If the user prefers to solve the equation using just the coefficients then a “Solve For:” button allows the problem to be setup using just the coefficients that allows the user to adjust the values until the correct equation results. Using the quadratic equation roots are calculated and displayed. A graph shows the actual curve and the user can manually change the scale to achieve the desired view. If the curve does not intersect the X axis the roots are said to be imaginary meaning there are no values for X that result in a Y = 0. This is all very confusing at first but this program helps to simplify by using adjuster inputs to see how changing the values affect the result and a graph of the actual curve. The equation changes as user inputs change along with the graphical output. Help and glossary screens are also provided to further help in understanding quadratic equations. When you are done simply Email the results to your home computer for further analysis. This program is a must for Students and Engineers. It makes the complex understandable. Simply the best factoring and quadratic equation program.
Features:
- Updates as You Edit
- Number Pad Digital Entry
- Solve for roots real or imaginary
- Calculates Curve shift right/left and up an down
- Calculates Maximum or Minimum value
- Graphs the actual curve to visually relate the equation.
- Help Screen, Glossary and Email
Example:
The equation takes the form of y = ax^2 +bx + c. Note that there is a square term x^2 with a coefficient of "a" and an "x" term with a coefficient "b" and a constant "c". They are u-shaped curves either convex or concave in shape. Solving them in the the conventional sense means finding the roots. The roots are the "y" values for which x = 0. Note that if the curve lies above the x axis there are no real roots because the curve does not pass through y = 0. In the example the "Factor" method is used to solve for roots. You can as easily solve for roots using the "Coefficient" method by selecting the "Solve for" button.
This app was developed by Raymond Seymour, after working at General Electric for 37 years he’s now making Engineering apps for iOS. As an inventor he has over 60 granted U.S. Patents.