The expression that is most useful for finding the year where the population was at a minimum would be 8 (x - 4)² + 592.
Given expression 8x² − 64x + 720 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998.
A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given expression is 8x² − 64x + 720
Let y = 8x² − 64x + 720
also, y - 720 = 8x² - 64x
by Extracting common factor 8 on the right side
y - 720 = 8(x² - 8x)
Add (8/2)² on both side, we get
y - 720 + 8(8/2)² = 8 (x² - 8x + 4²)
y - 720 + 128 = 8 (x² - 8x + 16)
on simplification
y - 592 = 8 (x - 4)²
y = 8(x - 4)² + 592
therefore, y = 8 (x - 4)² + 592
The expression that is most useful for finding the year where the population was at a minimum would be 8 (x - 4)² + 592.
Learn more about a quadratic equation here:
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