4 5 Solving Quadratic Equations by Finding Square
4. 5 Solving Quadratic Equations by Finding Square Roots
How would you solve the equation: x 2 = 4 (take the square root of each side!) * Remember, the square root of a positive # has 2 answers! (one + and one -)
Radical sign Radicand
Properties of Square Roots (a>0 and b>0) 1. Product Property – 2. Quotient Property. Example:
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) Just multiply the top & bottom of the fraction by the radical to “rationalize” the denominator.
More Examples! 1. Can’t have a tent in the basement! 2.
Conjugates • The product of 2 conjugates is always a rational number.
Rationalizing with Conjugates •
Rationalizing with Conjugates • 34
Solving Quadratic Equations 1. Solve. 3 - 5 x 2 = -9 -3 -3 -5 x 2 = -12 -5 -5 x 2 = 2. Solve. 3(x-2)2=21 3 3 (x-2)2 = 7
More Examples! 3. Solve. 4 x 2 -6=42 +6 +6 4 x 2=48 4 4 x 2 = 12 4. Solve.
Falling Objects! • Use h = -16 t 2 + h 0 Height of the object after it has fallen # of seconds after the object is dropped Object’s initial height
Example • 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?
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