Question

Emily invested in Google Stock (in the thousands of dollars) between the years 2000- 2013. The value of the stock can be modeled by the equation c(t)=t^2 -10t+76, where t=0 represents 2000. In what year did the stock reach its minimum value? What is the minimum value?

Answer 1

To find it, evaluate it at the endpoints and the vertex
in form
f(x)=ax²+bx+c
the x value of the vertex is -b/2a


given
c(t)=1t²-10t+76
x value of vertex is -(-10)/1=10


evaluate c(0) and c(13) and c(10)
c(0)=76
c(13)=115
c(10)=76

it reached minimum in 2000 and 2010
porbably teacher wants 2010
the min value is $76