# 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.

You have to solve 3 equations pretty much simultaneously here using the x and y values in the general form of the quadratic equation [latex]y=a x^{2} +bx+c[/latex] Start with the first values of x=0 and y=5.1 to solve for c: [latex]5.1=a(0) ^{2} +b(0)+c[/latex] so c = 5.1 Next use the second x and y values along with the value of c in the next equation: [latex]3.03=a(1) ^{2} +b(1)+5.1[/latex] 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: [latex]1.17=a(3) ^{2} +b(3)+5.1[/latex] 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: [latex]y=.38 x^{2} -2.45x+5.1[/latex]