Question

The 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. Choose the equivalent expression that is most useful for finding the year where the population was at a minimum.

Answer 1

Answer:

$8(x-4)^{2}+592$

Step-by-step explanation:

we have

The expression  $8x^{2} -64x+720$

This is a vertical parabola open upward

The vertex is a minimum

Convert the expression in vertex form

Factor the leading coefficient

$8(x^{2} -8x)+720$

Complete the square

$8(x^{2} -8x+16)+720-128$

$8(x^{2} -8x+16)+592$

Rewrite as perfect squares

$8(x-4)^{2}+592$

The vertex is the point (4,592)

That means -----> 4 years since 1998 the population has a minimum