Question

Aisha and Tatia awoke in their apartment one morning to find a broken water pipe had been leaking, making a growing circular water stain on their ceiling. As one does, Aisha and Tatia began tracking the area of water damage as a function A(t), in square inches, over time t, in hours, while waiting for someone to arrive to stop the leaking pipe.

Hour
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Area of Water Damage (in^2)
15 16 21 20 24 27 28 35 36 41 43 50 57 62 68

Q1: Since the water damage was making a circular water stain on their ceiling and knowing A = πr^2 gives the area of circle, Aisha thought a quadratic polynomial would be an appropriate function to model this event. Use the data at t = 1, 8, and 15 to create a quadratic function to model growing water damage.

-how am I supposed to make a quadratic function when the table values are not quadratic?

Answer 1

15 16 21 20 24 27 28 35 36 41 43 50 57 62 68
first differences:
1,5,-1,4,3,1,7,1,5,2,7,7,5,6
Doesn't look very quadratic to me; the 2nd differences will not be constant
However, given the three points, use them do determine the coefficients in
y = x^2+bx+c.
For example, (1,15) yields
a+b+c = 15
and similarly for the other two points.