Graphed Quadratics

[mikekg]

How do you, if you are looking at a graph which has a graph of a simple quadratic equation eg (ax+c), determine the equation without trial and error? Is there a reliable way?

 

[tkhunny]

Absolutely, unless all you have is rumor and inuendo.

Give an example and demonstrate how far you can get.

 

[mikekg]

Absolutely, unless all you have is rumor and inuendo.

Give an example and demonstrate how far you can get.

Oh, I just need help getting started. I don't know how to make a graph in this text box, but the visible points are (-3,-1),(0,2), and (3,-1)

 

[mmm4444bot]

a simple quadratic equation eg (ax+c) Whoops!

ax + c is not an example of a quadratic polynomial. It's linear because x is to the first power.

Using symbolic parameters A, B, and C, a quadratic polynomial takes the form Ax^2 + Bx + C. (Note that the highest power of x is a square -- that's quadratic).

If the parameter B = 0, then the quadratic takes the form Ax^2 + C.

You asked about reliability in finding the parameters A, B, and C from a graph. I would say that the reliability depends upon the quality of the graph. In other words, you need to be able to determine coordinates of three points through which the graph passes, and if you have to quess at the coordinates because you can't tell exactly what they are, then your result is only as good as your guesses.

The process involves solving a system of three equations for A, B, and C. You create the system by substituting the x- and y-values from three points into the equation:

y = Ax^2 + Bx + C

Of course, if the graph is for something like y = x^2 + 1, you can reason it out without resorting to a system of equations, by inspection.

Please show your work thus far, if you would like to discuss a specific exercise.

Cheers ~ Mark