How does a,b,c change ax squared + bx + c (when graphing)??

Question

How does the graph change when "a" changes?
How does the graph change when "b" changes?
How does the graph change when "c" changes?
Additionally and most importantly how can i proves this?? thanks to anyone who can solve this.

Answer 1

Assuming, a,b & c are not all zero, consider the cases for all combinations:

Case1: a is nonzero, then consider each of the following,

(i) if b=c=0; then ax^2 is a parabola w/vertex at (0,0). If a> 0 the parabola upens up; otherwise it opens down.
(ii) if b=0, then ax^2 + c. The vertex of this parabola is (0,c), showing a vertical shift.
(iii) if c=0, then ax^2 + bx .....
:
:

Answer 2

There is another way to look at this. At x = 0, y = c, so the curve crosses the y axis at y = c. The minimum value of the curve occurs when dy/dx = 0, or 2ax+b=0, or where x =-b/2a. For very large values of x, the equation approximates y = ax^2 which is a concave-upward parabola, which narrows as a increases.

Answer 3

hey....you're letting us solve your homework, ei?

you need a graphing paper;
make a graph with b and c as constants and a as unknown - use succeeding numbers for a such as 1, 2, 3, or 10, 20, 30
do the same way using b as unknown, a and c as constants;
repeat using c as unknown, a and b as constants.

not only will you see the graph, but also will prove that you did it.

good luck to being an engineer.....lol