Answer:

Step-by-step explanation:
Calculate the distance d using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (6, - 2)
d = 
= 
= 
=
← exact distance
Because this is a positive parabola, it opens upwards, like a cup, and the vertex dictates what the minimum value of the function is. In order to determine the vertex, I recommend completing the square. Do that by first setting the function equal to 0 and then moving the 9 to the other side by subtraction. So far:

. Now, to complete the square, take half the linear term, square it, and add that number to both sides. Our linear term is 6. Half of 6 is 3 and 3 squared is 9. So add 9 to both sides.

. The right side reduces to 0, and the left side simplifies to the perfect square binomial we created while completing this process.

. Move the 0 back over and the vertex is clear now. It is (-3, 0). Therefore, 0 is the minimum point on your graph. The first choice above is the one you want.
Answer:
B. 15c > 1,800 + 10c
Step-by-step explanation:
Profit=Total revenue - total cost
Profit is achieved:
when total revenue is greater than total cost
TR>TC
Or
When total cost is less than total revenue
TC<TR
From the question
Total cost=1800+10c
Total revenue=15c
Profit=TR>TC or TC<TR
15c>1800+10c
Or
1800+10c<15c
Option B. 15c > 1,800 + 10c satisfies the condition that Profit=TR>TC