Question

Please answer 1,2 and 3!! Thank you

Answer 1

1. The constant term is 16

`f(x) = {x}^(2) + 8x + 16 - 16- 15`

2.

`f(x) =( {x}^(2) + 8x + 16 )- 16- 15`

3.

`f(x) = {(x + 4)}^(2) - 31`

Explanation:

The given quadratic trinomial is

`f(x) = {x}^(2) + 8x - 15`

The coefficient of x is 8. Half of 8 is 4.

The square of 4 is 16.

We add and subtract 16 to get;

`f(x) = {x}^(2) + 8x + 16 - 16- 15`

The first three terms make a perfect square:

`f(x) =( {x}^(2) + 8x + 16 )- 16- 15`

We now factor the perfect square and collect like terms to get:

`f(x) = {(x + 4)}^(2) - 31`

This is called the vertex form.