# Quadratic with simple meaningful intuitive constants

• B
• PaulDiddams
In summary, the speakers discuss a simple quadratic rearrangement that uses the intercept and the values of x and y to drive the quadratic function, instead of traditional a, b, and c constants. The speaker suggests naming this rearrangement after themselves and mentions its usefulness and uniqueness. However, the other speaker reminds them that naming things after themselves is frowned upon.
PaulDiddams
TL;DR Summary
A simple quadratic rearrangement that uses the intercept and the values of x and y that define the maxima or minima, in place of a, b and c, to drive a quadratic function. (demo Excel sheet attached).

Tweaking the a, b and c constants to fit new observed data is a bit of a pain.

When I was a grad. student I came up with the following simple quadratic rearrangement that uses the intercept (Yo) and the values of x and y that define the maxima or minima (Xm, Ym) in place of non-intuitive a, b and c constants to drive the quadratic function. I also include rearrangements to calculate x from y, or Yo which I often find very useful too.

I would appreciate being credited "Diddams equation" if you choose to use my rearrangement. I think it's really neat and very powerful.

Enjoy.

#### Attachments

• Diddams Equation Demo.xlsx
18.4 KB · Views: 93
That's a simple rearrangement exercise for high school, done millions of times before.
Naming things after yourself is frowned upon by the way. Even if it were something new.

mfb said:
That's a simple rearrangement exercise for high school, done millions of times before.
Naming things after yourself is frowned upon by the way. Even if it were something new.
I've been using this rearrangement for over 30 years now and neither I nor anyone I know has ever seen it done before, and my colleagues have been referring to it by that name for point of reference. If you have references where it's been done and shared before I'm interested to see them.

## 1. What is a quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared. It can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

## 2. What are the roots of a quadratic equation?

The roots of a quadratic equation are the values of x that make the equation equal to 0. They can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.

## 3. What is the discriminant of a quadratic equation?

The discriminant is the part of the quadratic formula under the square root sign, b^2 - 4ac. It can be used to determine the nature of the roots of a quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If it is zero, the equation has one real root. And if it is negative, the equation has two complex roots.

## 4. How can quadratic equations be solved graphically?

Quadratic equations can be solved graphically by graphing the equation on a coordinate plane and finding the x-intercepts, which are the points where the graph crosses the x-axis. These points correspond to the roots of the equation.

## 5. What are some real-life applications of quadratic equations?

Quadratic equations have many real-life applications, such as in physics to model the motion of objects under gravity, in engineering to design structures and machines, and in business to analyze profit and loss. They can also be used to solve problems in geometry and optimization.

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