ANSWER

EXPLANATION
The given function is:

Factor -3 for the first 2 terms.

We add and subtract the square of the coefficient of x.

Factor the perfect square trinomial.

The vertex form is:

 
        
             
        
        
        
Answer:
-12, -14, 34
Step-by-step explanation:
 
        
             
        
        
        
Answer:
34
Step-by-step explanation:
16+10+6=34
 
        
             
        
        
        
Answer:
<h2>
4773 peoples.</h2>
Step-by-step explanation:
Given the number of people d, in thousands applying for medical benefits per week in a particular city c modeled by the equation d(t)=2.5 sin(0.76t+0.3)+3.8 where t is the time in years, the maximum number of people tat will apply will occur at d(t)/dt = 0
Differentiating the function given with respect to t, we will have;

First we need to know that differential of any constant is zero.

If  then;
 then;
 
To know the maximum number of people in thousands that apply for benefits per year in the city, we wil substitute the value of t = 29.75 into the modeled equation

Since d is in thousands, the maximum number of people in thousands will be 4.7732*1000 = 4773.2 which is approximately 4773 peoples.