Solving Quadratic Equations by Finding Square Roots

Square Roots Square roots: a number that produces a specified quantity when multiplied by itself. Example: 49 = 7  (7 × 7 = 49) Types of square roots: Positive: 81 = 9 Negative: − 100 = -10 Zero Square Root: 0 = 0 Two square roots: ± 0.25 = ±0.5 Undefined: −4 (no square root)

Perfect Squares Perfect Squares: numbers whose square roots are integers. 82 64 92 81 102 100 112 121 122 144 132 169 142 196 152 225 12 1 22 4 32 9 42 16 52 25 62 36 72 49

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: 5 or 12

Evaluating Square Roots − 121 1.44 0.09 7

Evaluating a Radical Expression When a = 1, b = -2 and c = -3, evaluate: 𝑏 2 −4𝑎𝑐

Evaluating a Radical Expression When a = 2, b = 4 10±2 𝑏 𝑎

Falling Object Model Formula: ℎ=−16 𝑡 2 +s h = ground level t = time s = 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.

Homework Page: 507 8-20 evens and 36, 38.