Answer:
8(x^2 − 22x + 128)
Step-by-step explanation:
8(x^2 − 22x + 128) Take 8 as a common factor
The equivalent expression that is most useful to find the year where the population is minimum is, 8(x-11)^2+56
A quadratic equation is an algebraic expression of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a, b are the coefficients, x is the variable, and c is the constant term
Given an expression that represents the population from 1998 to 2018,
[tex]8x^2-176x+1024[/tex]
Let,
[tex]y=8x^2-176x+1024[/tex]
Which is an upward parabola,
Since, the minimum value of an upward parabola,
[tex]y=a(x-h)^2+k[/tex]
is find at x = h,
From equation (1),
[tex]y=8x^2-176x+1024[/tex]
[tex]y=8x^2-176x+968-968+1024[/tex]
[tex]y=8(x^2-22x+121)+56[/tex]
[tex]y=8(x-11)^2+56[/tex]
By comparing,
The population is minimum at x = 11. ( that is after 11 years since 1998 )
Hence, the equivalent expression that is most useful to find the year where the population is minimum is,8(x-11)^2+56
To know more about quadratic equations follow
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