Question

In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

Find a quadratic model for the data in the table. Type your answer below. Show your work.

Answer 1

You have to solve 3 equations pretty much simultaneously here using the x and y values in the general form of the quadratic equation
`y=a x^(2) +bx+c`
Start with the first values of x=0 and y=5.1 to solve for c:

`5.1=a(0) ^(2) +b(0)+c` so c = 5.1
Next use the second x and y values along with the value of c in the next equation:

`3.03=a(1) ^(2) +b(1)+5.1` gives you
-2.07 = a + b. Solve this for a:
a = -2.07 - b
Finally use the third set of numbers with the c value AND the subbed value for a:

`1.17=a(3) ^(2) +b(3)+5.1`
1.17 = 9(-2.07 - b)+ 3b + 5.1 which simplifies to:
1.17 = -18.63 - 9b + 3b + 5.1 which further simplifies to:
14.7 = -6b and b = -2.45
Now you have c and b, let's find a using one of the simplified equations:
-2.07 = a + b
-2.07 = a - 2.45
a = .38
So here's your equation:

`y=.38 x^(2) -2.45x+5.1`