5.3 Solving Quadratic Equations by Finding Square Roots

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5.3 Solving Quadratic Equations by Finding Square Roots (p. 264)

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5.3 Solving Quadratic Equations by Finding Square Roots OBJ: To solve quadratic equations by finding square roots and model real-life problems 5.3 Solving Quadratic Equations by Finding Square Roots Do Now: How would you solve the equation x2 = 100 ?

How would you solve the equation: x2 = 4 (take the square root of each side) * Remember, the square root of a positive # has 2 answers! (one + and one -)

Radical Radical sign Radicand

Properties of Square Roots Product Property Like: Quotient Property Like:

Examples: 1. 2. 3.

Rationalizing the Denominator You CANNOT leave a radical in the denominator of a fraction! No tents in the basement!!!! (the numerator is OK) To “rationalize” the denominator: multiply the top & bottom of the fraction by the radical

Can’t have a tent in the basement! Examples: 4. 5. Can’t have a tent in the basement!

Solving Quadratic Equations 6. 3 - 5x2 = -9 -3 -3 -5x2 = -12 -5 -5 x2 = 7. 3(x-2)2=21 3 3 (x-2)2 = 7

9. 8. 4x2-6=42 +6 +6 4x2=48 4 4 x2 = 12

Falling Objects! Use h = -16t2 + h0 Height of the object after it has fallen Object’s initial height # of seconds after the object is dropped

Ex 10: The tallest building in the USA is in Chicago, Illinois. It is 1450 ft. tall. How long would it take a penny to drop from the top of the building to the ground?