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5-35-3Solving Quadratic Equations by Solving Quadratic Equations by
finding Square Roots.finding Square Roots.
Objective: Solve quadratic functions by finding square roots.
Properties of Square Roots (a > 0, b > 0)
Product Property : ab a b
Quotient Property:a a
b b
A square root expression is considered simplified IF:
2. There is no radical in the denominator.
1. No radicand has a perfect square root factor other than 1
EXAMPLES: Simplify the expressions:
24 4 6 2 6
7
16
7 7 7
2 2 44 4
7
2
7 2 14
22 2
Example 1: Solve 22 1 17x
2
2
2 16
8
8
4 2
2 2
x
x
x
x
x
Example 2: Solving a Quadratic Equation
Solve: 215 7
3x
25 21
5 21
5 21
x
x
x
Homework:
Page 267: #19-47 EOO
BRING BOOKS TOMORROW
IN-CLASS TOMORROW:
P.267-268 #51- 67 ODD
Example 4When an object is dropped, its speed continually increases, and therefore its height above ground decreases at a faster and faster rate.The height h (in feet) of the object t seconds after it is dropped is modeled by the function
216 oh t h
Where ho is the initial height
The tallest building in the United States is in Chicago. It is 1450 feet talla) How long would it take a penny to drop from the top of this building?
0
2
Let h initial height = 1450 ft.
16 oh t h
2
2
2
2
0 16 1450
1450 16
1450
16
90.625
90.625
9.5
t
t
t
t
t
t
b) How fast would the penny be traveling when it hits the ground if the speed is given by s=32t where t is the number of seconds since the penny was dropped.
32s t 32 9.5
304 ft/sec.
s
s
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