Equations

Full title	Equations
Year of release	2021
Publisher	Liddiard Computing
Producer / Author(s)	Roger Liddiard
Memory	19k
Type	Math's Utility
Cost :	PD - never sold
Download	Equations [CRC32 DA504644] Distribution Permission Allowed | Group 1

Instructions

  Equations draws graphs of linear(x), quadratic (X²) and cubic (X³) equations between specified limits of x. IT scales the values of x and y so the graphs exactly fill the screen. If the x and y axes are within range, these are also drawn.

  The program uses about 3k of memory. To load the program, enter LOAD EQUATIONS.   When loaded enter RUN.

The program will display a graph of the equation

           y = ax³+bx²+cx+d

and asks you to input the values of a, b, c and d and the upper and lower limits of x. These must be single length integers between -100 and +100 (i.e. whole numbers with no decimal points). The graph of this equation is then displayed along with the maximum and minimum - values of x and y. For accuracy the values of y are calculated using floating point arithmetic.

To display another equation, simply enter RUN. As an example try;

y = x³+ 3x²-6x-8

i.e. a =1, b = 3, c = -6, d = -8

Set the lower limit of x = -4, the upper limit of x=3

Finding the roots of a cubic equation

The roots of an equation are where its graph crosses the x-axis, i.e. y=0. A cubic equation (x³) always has at least one root. If the graph only crosses the x-axis once, no two roots are imaginary. If the graph crosses the x-axis three times (or just touches it), all the roots are real. To find the value of the roots, estimate the value of x where it crosses the x-axis (the range of x is rides into 64 squares wide). Then repeat the equation using a narrower range for the lower and upper limits of . This will give a more precise graph just where it Prasses the x-axis. This process can be repeated until Ha range of x equals 1 (the lowest range possible).

Screen shots

  

Tape Inlay

Cassette Body