Question

Plz help!

What is the constant of variation for the quadratic variation?

A. 5

B. 10

C. 15

D. 25

Answer 1

the correct answer to the problem is A or 5

Answer 2

dy/dx=25, 35, 45, 55

d2y/dx2=10,10,10 (this constant just proves that it is a quadratic relation)

Now we can set up a system of equations for ax^2+bx+c

16a+4b+c=80, 9a+3b+c=45, 4a+2b+c=20 getting differences

7a+b=35, 5a+b=25 and again

2a=10, a=5, making 7a+b=35 become:

7(5)+b-35, b=0, making 4a+2b+c=20 become:

4(5)+2(0)+c=20, c=0 so

y=5x^2

So the constant of variation for this quadratic is 5.