1. Warm-up 8-7
HW 99, #9
HW 99, #18

2. Lesson 8-7 Quadratic Variation
Objectives:
Students will:
Be able to find equations of direct, inverse, and joint quadratic variation
Solving problems involving quadratic variation

3. Quadratic Variation
3 possibilities
1) Direct → y = kx2
“y varies directly with the square of x”
2) Inverse →
“y varies inversely with the square of x”
3) Joint → y = kxz
“y varies jointly with x and z”

4. Writing Variation Equations
Choose equation
Decide x, y (and z)
Write general equation
Plug in values
Solve for k
Re-write equation with k-value

5. Example 1 Find the equation of variation where y varies inversely as the square of x, and y = 2 when x = 3.
Example 2 Find an equation of variation where y varies jointly as x and z, and y = 2, when x = 3, and z = 4.

6. Example 3 The intensity I of the light from a lamp varies directly as the wattage W of the lamp and inversely as the square of the distance D from the lamp. The intensity is 10 units when a 100-watt bulb is used at a distance of 20 feet. What is the intensity if a 75-watt bulb is used at 25 feet.
Example 4 The force of attraction F between two magnets varies inversely as the square of the distance D between them. The force is 5 newtons when the magnets are 2 cm apart. What is the force when the magnets are 5 cm apart?

7. HW 100