# 1.5 Solving Quadratic Equations by Finding Square Roots

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1.5 Solving Quadratic Equations by Finding Square Roots
(p. 32) How do you simplify radicals? What are the steps to rationalize a denominator? What is a conjugate? How many answers will you get when you solve a quadratic equation by finding square roots? Identify the formula h = −16t2 + h0?

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 -)

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!

Conjugates

Rationalize the denominator of fractions
SOLUTION

Guided Practice

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

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

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?