Ray Tools: Polynomial Equations

Understanding polynomial equations (equations with multiple x to the power of components) can be daunting but this program simplifies understanding. Both from an educational and an engineering standpoint where the user needs to understand the relationship between the coefficients and how the curve propegates 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^3 + bx^2 + cx + d“ Minimum and maximum points in the curve are calculated if they exist and are displayed. A trace function allows the user to visually scroll through the equation to find Roots where they exist. This is evident visually where Y = 0 and the curve crosses or intersects the X axis. 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. 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 unknown. The equation changes as user inputs change along with the graphical output. Help and glossary screens are also provided to further help in understanding polynomial 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.
- Calculates Maximum or Minimum value.
- Trace function solves for roots.
-Graphs the actual curve to visually relate the equation.
-Scroll through calculated results with trace function.
-Help Screen, Glossary and Email.

Example: Select the "Form" button and the expression is setup that allows you to adjust each of four coefficients to create the cubic polynomial equation. Note that there are adjustor buttons to increase or decrease each coefficient. You can as easily use the built-in keyboard by touching the input field. When starting to understand polynomials keep the values small so that the graphing provides more flexibility. So we have Y = 2X^3 + 10X^2 -14X + 6. It takes the form of y = ax^2 + bx^2 + cx + d where a = 2, b = 10, c = -14, d = 6. Look at the curve calculated from this equation and displayed below in the graph portion of the screen. Use the trace X value to scroll through the curve data finding Y values for X = 0 if your curve passes through the X axis. The program calculates the values where the minimum or maximum occurs. Simply plug this value into the trace X value to calculate the Y values for the minimum or maximum values.

Try changing the Solve for Button to Coefficients. Then use the adjuster buttons to change the coefficients for "a", "b", "c" and "d" values. Note how the screen displays the graph of the equation and that it intersects the x axis at two places. If the graph does not intersect the x axis. In this case the curve intersects the X axis at -6.206. The curve appears to cross at X = .5 but it rides above the X axis by 1.8. Sometimes cubic equations are divided by a factor (X + …) then the equation becomes a quadratic and is solved by the quadric formula for roots. I find it easier to use the trace feature to find roots if necessary.

Look for other Ray Tools app’s including linear, quadratic, exponential and logarithmic equations.

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.