Question

please answer 1,2 and 3!! Thank you

Answer 1

Answer:

1. The constant term is 16

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

2.

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

3.

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

Step-by-step 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.