5 3 solving quadratic equations by finding square roots
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5.3 Solving Quadratic Equations by Finding Square Roots

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5.3 Solving Quadratic Equations by Finding Square Roots. (p. 264). 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. Radical sign. Radicand. Properties of Square Roots.

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how would you solve the equation x 2 4 take the square root of each side
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

Radical sign

Radicand

properties of square roots
Properties of Square Roots

(a>0 and b>0)

  • Product Property –
  • Quotient Property-

Example:

Example:

examples
Examples

1.

2.

3.

rationalizing the denominator
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
More Examples!

1.

2.

Can’t have a tent in the basement!

solving quadratic equations
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

more examples1
More Examples!

4. Solve.

  • Solve. 4x2-6=42

+6 +6

4x2=48

4 4

x2 = 12

falling objects
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
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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