Was the quadratic function derived?By quadratic function, I mean : f ( x ) = a x 2 + b x + cBecause the specific constant have a different role, e.g. increasing a has a role of narrowing or inverting the parabola, I'm thinking if this was a derived function/equation. If so, how was this derived?Additionally, for an even more general equation of a circle for instance: x 2 + y 2 + D x + E y + F = 0What would be the role of each of the constants: D, E and F?And how can I go further into this?

Question

Was the quadratic function derived?By quadratic function, I mean :  f  (  x  )  =  a      x    2    +  b  x  +  cBecause the specific constant have a different role, e.g. increasing a has a role of narrowing or inverting the parabola, I&#039;m thinking if this was a derived function/equation. If so, how was this derived?Additionally, for an even more general equation of a circle for instance:      x    2    +      y    2    +  D  x  +  E  y  +  F  =  0What would be the role of each of the constants: D, E and F?And how can I go further into this?

Jovanni Salinas · Accepted Answer

Step 1I think you&#039;re seeing this the wrong way around. It wasn&#039;t that we chose the standard form   a      x    2    +  b  x  +  c because we could change the geometry. The choice was simply the most natural way of writing a quadratic.Step 2Once we had the most simple form, we then looked at the geometric implications of altering the constants.

Diego Barr · Accepted Answer

Step 1As for the additional part of your question, for the following equation of circle,      x    2    +      y    2    +  D  x  +  E  y  +  F  =  0the co-ordinates of the center of the circle are   (  −      D    2    ,  −      E    2    ) (the role of the constants D and E right there) and the radius of the circle is                     D        2            4        +                  E        2            4        −    F  ; so for fixed D and E, F is inversely proportional to the radius(size) of the circle.

Was the quadratic function derived? By quadratic function, I mean: f(x)=ax^2+bx+c. Because the specific constant have a different role, e.g. increasing a has a role of narrowing or inverting the parabola, I'm thinking if this was a derived function/equation. If so, how was this derived?

Answered question

Answer & Explanation

New Questions in Algebra I