### 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 (X^{2})
and cubic (X^{3}) 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 = ax^{3}+bx^{2}+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 = x^{3}+ 3x^{2}-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 (x^{3}) 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).