Quadratic Equations
(Lesson 2 – Completing the Square: Word Problems)
Maximum or Minimum value is the “y-part” of the vertex.
I.e. 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
Area Problem
A rectangular field is to be enclosed on one side by a barn and on the other three sides by 200 m of
fencing. Determine the dimensions of the field if the area is to be a maximum.
Revenue Problem
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?
Integers
Find two integers whose difference is 12 and whose product is a minimum.
Parabolic Flight
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?