Solving Quadratic Equations by Finding Square Roots
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Transcript of Solving Quadratic Equations by Finding Square Roots
Solving Quadratic Equations by Finding Square Roots
Square Roots
• Square roots: a number that produces a specified quantity when multiplied by itself.– Example: = 7 (7 × 7 = 49)
• Types of square roots:– Positive: = 9– Negative: = -10– Zero Square Root: = 0– Two square roots: = – Undefined: (no square root)
Perfect Squares
• Perfect Squares: numbers whose square roots are integers.
12 1
22 4
32 9
42 16
52 25
62 36
72 49
82 6492 81102 100112 121122 144132 169142 196152 225
Not Perfect Squares
• Numbers that are not perfect squares must be written using the radical symbol or approximated. These numbers are irrational.–Irrational Numbers: numbers that
cannot be written as fractions–Examples: or
Evaluating Square Roots
Evaluating a Radical Expression
When a = 1, b = -2 and c = -3, evaluate:
Evaluating a Radical Expression
When a = 2, b = 4
Falling Object ModelFormula:
h = ground levelt = times = initial height
h=−16 𝑡 2+s• An engineering student is in an “egg dropping
contest.” The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg’s container to hit the ground. Assume there is no air resistance. (h = 0 when it hits the ground)
h=−16 𝑡 2+s• An engineering student is in an “egg dropping
contest.” The goal is to create a container for an egg so it can be dropped from a height of 64 feet without breaking the egg. To the nearest tenth of a second, about how long will it take for the egg’s container to hit the ground. Assume there is no air resistance.
HomeworkPage: 507
8-20 evens and 36, 38.