MAT 150 – AlgebraClass #9Topics:

• Solving Quadratics by

• Factoring

• Square Root

• Completing the Square

• Quadratic Formula

• Solving quadratics having complex solutions

Ways to Solve a Quadratic Equation

1. The Quadratic Formula2. The Square Root Method3. Factoring

a. GCFb. Two Binomials c. Difference of 2 Squares

The QUADRATIC FORMULA

*In order for the quadratic formula to work, the equation MUST EQUAL 0!

The Quadratic Formula will find all x-values in any quadratic equation. On a graph, these would be the x-intercepts (zeros, roots).

This method will work for ALL quadratic equations!

Round to the nearest thousandth if necessary. Check your solutions using the graphing calculator.

A.

B.

Solve with the Quadratic Formula

This method can be used when b = 0.

A.

B. B.

Square Root Method

You will need to choose with method of factoring is appropriate. However, this method is usually faster than the Quadratic Formula.

A.

Solve with Factoring

Ex 4: Complex Solutions

A. B.

C. D.

Use any method to solve:

A.

B. B.

Ex 5: Solve the Quadratic Equations

Try to check your solutions on the graphing calculator. What do you notice about the graphs of these functions that is different from the other quadratic functions?

Discriminant

We can determine the type of solutions a quadratic equation has by looking at the expression which is called the discriminant.

If > 0, there are two different real solutions

If = 0, there is one real solutions

If , there is no real solutions (two complex solutions)

Body-Heat LossThe model for body-heat loss depends on the coefficient of convection K, which depends on the wind speed s according to the equation , where s is in miles per hour. Find the positive coefficient of convection when the wind speed is:

a.) 20 mph.

b.) 60 mph.

c.) What is the change in K from change in speed from 20 mph. to 60 mph?

Market Equilibrium

Suppose that the demand for artificial Christmas trees is given by the function and that the supply of these trees is given by where p is the price of a tree in dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold/bought at this price.

Assignment

Pg. 195-197

#1-3 all

#23-25 all

#31-33 all

#36-38 all

#47-48 all

#52, 53, 56, 59, 67