Chapter 4 Note Packet on Quadratic Functions and Factoring

Day 2: 4-3 Solve Solve x2 + bx + c = 0 by Factoring and 4-4 Solve ax2 + bx + c = 0 by Factoring

Example 3: Factor these expressions using special patterns

x2 - 81

m2 - 22m + 121

ZERO PRODUCT PROPERTY

If the ______of two expressions is zero, then ______or ______of the expressions equals zero.
Algebra / If A and B are expressions and AB = ____ , then A = _____ or B = _____ .
Example / If (x + 5)(x + 2) = 0, then x + 5 = 0 or x + 2 = 0. That is, x = ______or x = ______.

Example 4: Find the roots of the equation x2 - 2x - 15 = 0.

Example 5: Find the zeroes of the function x2 +7x -30 by rewriting the function in intercept form.

Solve ax2 + bx + c = 0 by Factoring

Example 8: Factor the expression using special patterns.

16x2 - 36

9y2 + 42y + 49

25t2 - 110t + 121
Factor out ______first.

Chapter 4 Note Packet on Quadratic Functions and Factoring

Day 3: 4-5 Solve Quadratic Equations by Finding Square Roots

Review Properties of Square Roots

PROPERTIES OF SQUARE ROOTS (a > 0, b> 0)

Example 1
Product Property / = _____ · ______/
Quotient Property / = /

Use properties of square roots

Example 2

a. = _____ · ______= _____

b. = _____ = _____ · ______= ______

c. = = _____

Rationalize denominators of fractions

Example 3

Simplify and

Solve a Quadratic Equation Using Square Roots

Example 4

Solve (x - 6)2 = 8. Solve 4(x - 1)2 = 8.

Chapter 4 Note Packet on Quadratic Functions and Factoring

Day 4: 4-7 Completing the square and Square root of -1 = i

Solve a quadratic equation

Example 2

Example 3

Write as a complex number in standard form.

a. (3 + 7i) - (8 - 2i)

b. (2 + 5i) + (7 - 2i)

c. (2 + i)(-5 + 2i)