Download Section 10.4-10.5 Guided Notes

Algebra I
Section 10.4 – 10.5: Solving Quadratic Equations
Spring 2017
Section 10.4 Recall:
Solving Quadratics (when b=0):
• Step 1: Isolate the term that is being square on one side of the equation.
• Step 2: Square root both sides of the equation.
• Step 3: Finish solving for x, if necessary.
Find the EXACT solutions to the following equations:
1.) (x + 5)2 +1 = 37
2.) (x - 6)2 - 14 = 3
3.) 2(x + 1)2 + 3 = 51
Standard Form of a Quadratic Function:
y = ax2 + bx + c
Standard Form of a Quadratic Equation:
0 = ax2 + bx + c
10.5 – Factoring to Solve Quadratic Equations:
Objective 1: Solving Quadratic Equations by Factoring
•
In the previous lesson, you solved quadratic equations by finding square roots. This only works when
__________. You can solve quadratic equations by using the Zero Product Property, if __________.
Key Concepts: Property – Zero-Product Property:

For ___________________ a and b, if ab = 0, then a = 0 or b = 0.
Example: If (x+3) (x+2) = 0, then x + 3 = 0 or x + 2 =0
Example 1: Using the Zero-Product Property
Solve each equation:
1.) (x + 3) (x – 8) = 0
x=
Quick Check #1:
2.) (4x + 7) (x – 6) = 0
3.) (3x – 1) (x + 11) = 0
x=
x=
Quick Check #2:
4.) 2x (x – 2) = 0
x=
^^ Answer: ____________________
•
You can also use the Zero-Product Property to solve equations of the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 if the quadratic
expression 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 can be factored.
Example 2: Solve for x by factoring
5.) 4𝑥 2 − 12𝑥 − 27
Quick Check #3: Solve for x by factoring
6.) 𝑥 2 − 8 = 2𝑥
7.) 7𝑥 2 − 21𝑥 = 0
8.) 6𝑥 2 + 5𝑥 − 21 = 0
9.) 3𝑥 2 − 11 = 2𝑥 2 − 4𝑥 + 1
10.) 2𝑥 3 − 5𝑥 2 = 18𝑥 − 45
HW #24: due tomorrow, April 24th!
Write it here: