Photo by Ahmed Asaker on Unsplash

More On Quartics Architecture

Designing Quartics To Meet Your Needs

Greg Oliver
3 min readSep 24, 2024

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Following earlier posts promoting function design for learning and skills development, rather than simply finding roots, this post furthers my earlier posts on the concepts of developing zones or domains for polynomial generics y=Ax⁴+Cx²+Dx+E with specified numbers of Real roots and Turning Points Tp’s commencing with Genetic parents y=Ax⁴+Cx²+E.

This post assumes math at the high school level.

Note: Throughout this post, where appropriate for simplicity, we use Ax⁴ coefficient A=1.

Design Specs

Create a domain inside 2 generic Polynomials y=x⁴+Cx²+Dx+E and y=x⁴+Cx²+Mx+E shown in black and blue respectively in Graph 1 where all the functions between the boundaries have 3 Tp’s and 2 roots. We keep both constants E=0 for concept simplicity.

Concept is envisaged in Graph 1 with such a domain shaded green.

The red function is Big M a genetic y=-3Ax⁴-Cx²+E which traces the Turning Points of all generics y=x⁴+Cx²+Dx+E. It is introduced in several of my earlier posts e.g.:

Quartic Polynomials With Specified Turning Points Using Big M

Designing Quartic Polynomials — Converging Turning Points

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Greg Oliver
Greg Oliver

Written by Greg Oliver

Melbourne Australia - retired engineer with a "Maths is Graphs" architectural approach to understanding functions.