LESSON 2 – COMPLETING THE SQUARE: WORD PROBLEMS
Maximum or Minimum value is the “𝑦-part” of the vertex.
For vertex (ℎ, 𝑘) the maximum or minimum value is k.
STEPS TO SOLVING MAXIMUM AND MINIMUM PROBLEMS:
1. Identify the variables
2. If necessary, draw a diagram or picture using the information given
3. Write an equation using the variables
4. Complete the square to find the vertex (ℎ, 𝑘)
5. The maximum or minimum value is 𝑘
Example ① A rectangular field is to be enclosed on one side by a barn and on the other three sides by 200m
of fencing. Determine the dimensions of the field if the area is to be a maximum.
Example ② A motel has 30 rooms. The owners decide to raise the price of each room from the current
price of $40. Every $2 increase in price results in one less room rented out. What price of each
room would maximize revenue?
Example ③ Find two integers whose difference is 12 and whose product is a minimum.
Example ④ Joshua threw a ball that traveled on a parabolic path and then landed on the ground. Its flight
is modeled by the equation, ℎ(𝑡) = −4.9𝑡 2 + 9.8𝑡 + 1.1, where time, t, is in seconds and
height, h , is in metres.
a) Determine the maximum height reached by the ball.
b) How long did it take to reach maximum height?
c) When will the ball hit the ground?