How would I describe what these do?

[QueekJJ]

So I was writing a school report for homework, and I then decided I want to explain what the different values in a function would do to a graph. Some of the simple ones I had was like linear functions using y=mx+c, where m changes the steepness of the line while c is where the line intercept the y-axis, or move the graph up or down.

I want to describe parabolas ( y = (ax+b)^2 + cx + d ), but i dont know how to explain it properly. The best i can do is:
a - Makes the graph wider or thinner
b - shift the graph left or right
c - does the same thing as b?
d - shift the graph up and down

Is there a better way to describe it?

 

[Dr.Peterson]

Only d does something really simple; the others all perform a relatively complicated action.

To make it easy to see, go to Desmos.com and paste in y = (ax+b)^2 + cx + d, letting it make a slider for each parameter. Then try changing one at a time. You'll find a subtle difference between b and c.

Was this form of the equation given to you to describe, or was that your own choice? There are better ways to handle a parabola. I myself would probably choose a(x-b)^2+c, if I had a choice. In that equation, each parameter has a clear, distinct meaning.