The expression 8x2 − 144x 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represent

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The expression 8x2 − 144x 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represent

s 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(x2 − 18x 108) 8(x2 − 18x) 108 8(x − 9)2 − 216 8(x − 9)2 216

Mathematics

1 answer:

Rzqust [24] · Answer 1 · 2023-07-10T00:54:59+03:00

The expression that is most useful for finding the year where the population was at a minimum would be 8(x − 9)² + 216.

Given expression 8x² − 144x + 864 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998.

<h3>What is a quadratic equation?</h3>

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 − 144x + 864

Let y = 8x² − 144x + 864

also, y - 864 = 8x² - 144x

by Extracting common factor 8 on the right side

y - 864 = 8(x² - 18x)

Add (18/2)² on both sides, we get

y - 864 + 8(18/2)² = 8 (x² - 18x + 81²)

y - 864 + 648 = 8 (x² - 8x + 9)

on simplification

y - 216 = 8 (x - 9)²

y = 8(x - 9)² + 216

therefore, y = 8 (x - 9)² + 216