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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 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
trees that will be sold/bought at this price.
Assignment
Pg. 195-197
#1-6 all
#23-26 all
#31-34 all
#36-38 all
#47-48 all
#52, 54, 56, 67