Hi,

1. Read the problem.

after t days, the number of bacteria per cubic centimetre is given by the expression B = 20t^2 - 120t + 200

in how many days will the number of bacteria be at its lowest?

 2. Select the unknown.

 

 3. Translate into an equation: 

Given: B = 20t^2 - 120t + 200  0r t^2 - 6t + 10 

 4. Use the rules to solve.

B = (t-3)^2 + 1 (found by Completing the Square)

Using the vertex form of a Parabola opening up(a>0) or down(a<0),  

where(h,k) is the vertex:  V = (3,1) 

 5. Verify the result 

By definition, V(3,1) is the low point of the "Bacteria Level" and t = 3days



B = 20t^2 - 120t + 200. 

B = t^2 - 6t + 10 = (t-3)^2 - 9 + 10 = (t-3)^2 + 1

B = (t-3)^2 + 1

B represents a Parabola Opening Upward, V = (3,1)

In  days, bacteria be at its lowest



 

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