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Solving Quadratic Equations through Square Roots in Real-Life Scenarios

Explore how to solve quadratic equations by finding square roots with real-life applications. Learn the product and quotient properties of square roots and how to rationalize denominators. Practice solving equations and applying concepts to falling object scenarios.

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Solving Quadratic Equations through Square Roots in Real-Life Scenarios

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  1. 5.3 Solving Quadratic Equations by Finding Square Roots Goals: 1. Solve quadratic equations by finding square roots 2. using quadratic models in real life For what purpose would you use the product or quotient properties of square roots when solving quadratic equations using square roots?

  2. 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 -)

  3. Radical Radical sign Radicand

  4. Properties of Square Roots (a>0 and b>0) • Product Property – • Quotient Property- Example: Example:

  5. Examples 1. 2. 3.

  6. Rationalizing the Denominator You CANNOT leave a radical in the denominator of a fraction! Just multiply the top & bottom of the fraction by the radical to “rationalize” the denominator.

  7. Examples 1. 2. Can’t have a radical in the denominator!

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

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

  10. 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

  11. 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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