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

8(x − 4)^2 + 592

Explanation:

I took the test and got it right

Answer 2

`8(x-4)^(2)+592`

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