4.5 Solving Quadratic Equations by Finding Square Roots

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4.5 Solving Quadratic Equations by Finding Square Roots

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 (a>0 and b>0) Product Property – Quotient Property- Example: 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.

Can’t have a tent in the basement! More Examples! 1. 2. Can’t have a tent in the basement!

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

More Examples! Solve. 4x2-6=42 +6 +6 4x2=48 4 4 x2 = 12 4. Solve.

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

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?