Please put as much step by step explanations as possible. If you decide to do it on paper and the take a picture of it, please make sure that the picture quality is good enough for me to see. Thank you!

1. A soccer player kicks a ball from the ground to a maximum height of 12 m. The high point in the trajectory of the ball occurs at a distance of 18 m from the kicker. On the downward path, another player heads the ball at a height of 2.2 m from the ground.

a. How far from the kicker in the line of the trajectory must a player be to head the ball as described?

A retail electronics chain makes a profit of $14 on every MP3 player of a certain brand the chain sells. Last month, the chain sold a total of 600 of these MP3 players nationwide. The marketing department suspects that for every $1 decrease in price, the chain would sell an additional 100 players. The marketing department is interested in maximizing the gross profit on this item.

gross profit = (profit on each MP3 player)(number of players sold)

Let y equal the gross profit, and let x equal the number of dollars the MP3 players are discounted.

The profit per MP3 player will then be (14 - x).

The function that models this situation can be written as: y = (14x - x)(600 + 100x)

a. Expand out the function for y, then convert to vertex form.

b. What is the maximum gross profit the chain can expect based on these estimates?

c. By how many dollars must the chain decrease the price to get that maximum gross profit?