Solve the equations 3,4 by factoring and complete the square.

Solve the questions 2,6,7,9 by Quadratic .

Don't forget to write the let statements , and solve the qestions step by step.

And there is the answer questions at the bottom

WORKSHEET: Optimization Problems 2. A rocket is fired down a practice range. The height of the rocket in metres after t seconds is given by h = -_ + 31 + 45. Find the maximum height attained by the rocket. 3. Find two numbers whose difference is 10 and whose product is a minimum. 4. Find two numbers whose sum is 120 and whose product is a maximum. 6. Brett uses zau metres of rope to mark off a rectangular swimming area at a beach. No rope is used on the side that is the shore. What is the greatest area that can be enclosed, and what are its dimensions? 7. A theatre seats 4 000 people and charges $20 per ticket. At this price, all the tickets are sold. A survey indicates that if the ticket price is increased, the number of tickets sold will decrease by 200 for every $2 increase. What ticket price will result in the greatest revenue? 9. The cost of a ticket to a hockey arena seating 800 people is $12. At this price, every ticket is sold. Rachel conducts a survey, which indicates that if the price is increased, the attendance will fall by 100 for each $4 increase. What ticket price results in the greatest revenue? What is the greatest revenue? Answers: 2. 54 m 3.5, - 5 4. 60, 60 6. 7200 m' (120 m by 60 m) 7. $30 9. $22, $12 100