1. Ch3/4 Lesson 8 Solve Equations by Completing the Square Max/Min Problems

2. Why Use “Completing the Square”
“Completing the Square” is a process that converts a quadratic function that can not be factored to a form that can be solved algebraically
Suppose we have the following trinomial
If we complete the square, we end up with the expression on the right
Can’t factor this…
We end up with two answers in radical form

3. Practice: Solve for ‘x’ in exact form:

4. Ex: Solve by Completing the Square
Bracket the first two terms!
Divide the second term by 2 and square it! Purpose: Make the expression in the bracket into a perfect square!
Take the negative square outside of the brackets!
The trinomial becomes two equal binomials
Now you can solve this equation by square rooting both sides:

5. Practice: Solve for “x” by CTS
Bracket the first two terms!
Factor out any coefficient for x2
Divide the second term by 2 and square it!
Take the negative square outside of the brackets and multiply with coefficient in front!
The trinomial becomes two equal binomials
Solve for “x” by square rooting both sides

6. Ex: The height, “h” metres, of an infield fly ball “t” seconds after being hit is given by simplified formula : h = 30t – 5t2. How long after being hit is the ball at a height of 18 m?

7. Ex: The sum of two numbers is 80. Their product is 1500
Ex: The sum of two numbers is 80. Their product is Find the numbers
There are two numbers, let ‘x’ and ’80 –x’ be the numbers
Gather Information
80 minus the first number gives you the second nunber
The product is 1500
The two numbers are 30 and 80

8. Ex: A gardener would like to build a pathway of equal width around a rectangular garden measuring 8 meters by 15 meters. If this doubles the total area, then what is the width of the pathway?
x = – is call an extraneous root.

9. Ex: The difference of two numbers is 10. The sum of their squares is 60. Find the numbers
The second number is 10 more than the first
Gather Information
The sum of their squares is 60
The two sets of numbers are: