MAT 150 – Algebra Class #9

• • Topics: 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 Formula 2. The Square Root Method 3. Factoring a. GCF b. Two Binomials c. Difference of 2 Squares

The QUADRATIC FORMULA 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!

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

Solve with the Quadratic Formula

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

A. −3𝑥 2 + 4𝑥 + 6 = 0 B. 2𝑥 2 − 6 = 𝑥

Square Root Method

 This method can be used when b = 0.

A.

2𝑥 2 − 16 = 0 B.

B. 𝑥 − 6 2 = 18



Solve with Factoring

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

A.

𝑥 2 + 4𝑥 − 5 = 0 B.

3𝑥 2 + 7𝑥 = 6 C.

3𝑥 2 − 9𝑥 = 0

Complex Solutions

A.

𝑥 2 − 3𝑥 + 5 = 0 B.

3𝑥 2 + 4𝑥 = −3

Discriminant

 We can determine the type of solutions a quadratic equation has by looking at the expression 𝑏 2 − 4𝑎𝑐, which is called the discriminant.  If 𝑏 2 − 4𝑎𝑐 > 0, there are two different real solutions  If 𝑏 2 − 4𝑎𝑐 = 0, there is one real solutions  If 𝑏 2 − 4𝑎𝑐 < 0 , there is no real solutions (two complex solutions)

Market Equilibrium

Suppose that the demand for artificial Christmas trees is given by the function 𝑝 = 109.70 − 0.10𝑞 and that the supply of these trees is given by 𝑝 = 0.01 𝑞 trees that will be sold/bought at this price.

2 + 5.91

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

Assignment

Pg. 195-197 #1-6 all #23-26 all #31-34 all #36-38 all #47-48 all #52, 54, 56, 67