|Year of release||2021|
|Producer / Author(s)||Roger Liddiard|
|Cost :||PD - never sold|
Distribution Permission Allowed | Group 1
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).