The expression 8x2 − 176x + 1,024 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998. choose the equivalent expression that is most useful for finding the year where the population was at a minimum.
8(x − 11)^2 − 56
8(x − 11)^2 + 56
8(x2 − 22x + 128)
8(x2 − 22x) + 128

Step-by-step explanation:

We are given that an expression used to approximate small town's population in thousands from 1998 to 2018

Where x represents the number of years

We have to find the equivalent expression which is most useful for finding the year where the population was at a minimum.

Let y=

By using identity

By compare with

(h,k)=Vertex of parabola

The value of y =k is minimum at x=h

We get (h,k)=(11,56)

Substitute x=11

At x=11 the population  is minimum

Therefore,

Hence, this is required expression which is equivalent to given expression and most useful for finding the year where the population was at a minimum.

p = 6s

step-by-step explanation: