Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum » !Ignotum/Formulae/Quad
!Ignotum/Formulae/Quad
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum |
| Filename: | !Ignotum/Formulae/Quad |
| Read OK: | ✔ |
| File size: | 0288 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Quadratics x=(-b�(b�-4ac)^�)/2a This is called the quadratic formula where ax�+bx+c=0. It can give two answers (because of the �). If the curve y=ax�+bx+c was plotted then it would cross the x-axis at these values of x. y=(4ac-b�)/4a Where: y=y co-ordinate of the peak of the graph (highest/lowest point on the curve) a, b and c come from the general quadratic, y=ax�+bx+c x=-b/2a An equation for the line of symmetry of the curve is formed where a, b and c are from the general quadratic, y=ax�+bx+c.
00000000 23 20 4d 61 74 68 73 20 3e 20 51 75 61 64 72 61 |# Maths > Quadra| 00000010 74 69 63 73 0a 78 3d 28 2d 62 b1 28 62 b2 2d 34 |tics.x=(-b.(b.-4| 00000020 61 63 29 5e bd 29 2f 32 61 0a 54 68 69 73 20 69 |ac)^.)/2a.This i| 00000030 73 20 63 61 6c 6c 65 64 20 74 68 65 20 71 75 61 |s called the qua| 00000040 64 72 61 74 69 63 20 66 6f 72 6d 75 6c 61 20 77 |dratic formula w| 00000050 68 65 72 65 0a 61 78 b2 2b 62 78 2b 63 3d 30 2e |here.ax.+bx+c=0.| 00000060 20 49 74 20 63 61 6e 20 67 69 76 65 20 74 77 6f | It can give two| 00000070 20 61 6e 73 77 65 72 73 0a 28 62 65 63 61 75 73 | answers.(becaus| 00000080 65 20 6f 66 20 74 68 65 20 b1 29 2e 20 49 66 20 |e of the .). If | 00000090 74 68 65 20 63 75 72 76 65 20 0a 79 3d 61 78 b2 |the curve .y=ax.| 000000a0 2b 62 78 2b 63 20 77 61 73 20 70 6c 6f 74 74 65 |+bx+c was plotte| 000000b0 64 20 74 68 65 6e 20 69 74 20 77 6f 75 6c 64 20 |d then it would | 000000c0 63 72 6f 73 73 0a 74 68 65 20 78 2d 61 78 69 73 |cross.the x-axis| 000000d0 20 61 74 20 74 68 65 73 65 20 76 61 6c 75 65 73 | at these values| 000000e0 20 6f 66 20 78 2e 0a 79 3d 28 34 61 63 2d 62 b2 | of x..y=(4ac-b.| 000000f0 29 2f 34 61 0a 57 68 65 72 65 3a 0a 79 3d 79 20 |)/4a.Where:.y=y | 00000100 63 6f 2d 6f 72 64 69 6e 61 74 65 20 6f 66 20 74 |co-ordinate of t| 00000110 68 65 20 70 65 61 6b 20 6f 66 20 74 68 65 20 67 |he peak of the g| 00000120 72 61 70 68 0a 28 68 69 67 68 65 73 74 2f 6c 6f |raph.(highest/lo| 00000130 77 65 73 74 20 70 6f 69 6e 74 20 6f 6e 20 74 68 |west point on th| 00000140 65 20 63 75 72 76 65 29 0a 61 2c 20 62 20 61 6e |e curve).a, b an| 00000150 64 20 63 20 63 6f 6d 65 20 66 72 6f 6d 20 74 68 |d c come from th| 00000160 65 20 67 65 6e 65 72 61 6c 20 0a 71 75 61 64 72 |e general .quadr| 00000170 61 74 69 63 2c 20 79 3d 61 78 b2 2b 62 78 2b 63 |atic, y=ax.+bx+c| 00000180 0a 78 3d 2d 62 2f 32 61 0a 41 6e 20 65 71 75 61 |.x=-b/2a.An equa| 00000190 74 69 6f 6e 20 66 6f 72 20 74 68 65 20 6c 69 6e |tion for the lin| 000001a0 65 20 6f 66 20 73 79 6d 6d 65 74 72 79 20 6f 66 |e of symmetry of| 000001b0 0a 74 68 65 20 63 75 72 76 65 20 69 73 20 66 6f |.the curve is fo| 000001c0 72 6d 65 64 20 77 68 65 72 65 20 61 2c 20 62 20 |rmed where a, b | 000001d0 61 6e 64 20 63 20 61 72 65 0a 66 72 6f 6d 20 74 |and c are.from t| 000001e0 68 65 20 67 65 6e 65 72 61 6c 20 71 75 61 64 72 |he general quadr| 000001f0 61 74 69 63 2c 20 79 3d 61 78 b2 2b 62 78 2b 63 |atic, y=ax.+bx+c| 00000200 2e 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| 00000210 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 00000280 0a 0a 0a 0a 0a 0a 0a 0a |........| 00000288
.