Choosing an Appropriate Method

1
Choosing an Appropriate Method
2
Ways to Solve Quadratic Equations

• Square Root Method
• Graphing
• Quadratic Formula
• Factoring
• Completing the Square

3
Graphing

• Use if you have a graphing calculator handy.

4
Square Root Method

• Use if the equation has only an x2 term and a
  constant.

5
Factoring

• Use if you can factor the equation easily.

6
Quadratic Formula

• Use if you cannot factor the equation or if you
  are using a scientific calculator.

7
Completing The Square

• Use if a is 1 and b is even.

8
Which would you use?

• 2x2 6 0
• 25x2 36 0
• 2x2 7x 15 0
• 9x2 24x 16 0
• 6x2 5x 6 0
• 16x2 96x 135 0

9
Example

• A fountain has dimensions w and 2w. The concrete
  walkway around it is 4 feet wide. Together, the
  fountain and the walkway cover 1500 ft2 of land.
  Find the dimensions of the fountain.

10
Example 2

• A square pool has length p. The border of the
  pool is one foot wide. The combined area of the
  pool and the border is 400 ft2. Find the area of
  the pool.

11
Another Example

• Find all the values of x such that rectangle ACDG
  below has an area of 70 square units AND
  rectangle ABEF has an area of 72 square units.

C
D
2 3 x
E
B
x 2 2
A
F
G