Solving quadratics with square roots
-
Upload
swartzje -
Category
Technology
-
view
531 -
download
5
Transcript of Solving quadratics with square roots
![Page 1: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/1.jpg)
4.54.5Solving Quadratic Equations Solving Quadratic Equations
by Finding Square Rootsby Finding Square Roots
(p. 250-253)(p. 250-253)
![Page 2: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/2.jpg)
How would you solve the equation:How would you solve the equation:xx22 = 4 = 4
(take the square root of each side!)(take the square root of each side!)
* Remember, the square root of a positive # has 2 answers! (one + and one -)
*2- 2
4
4
2
2
orx
x
x
![Page 3: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/3.jpg)
RadicalRadical
3Radical Radical
signsignRadicandRadicand
![Page 4: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/4.jpg)
Properties of Square RootsProperties of Square Roots
(a>0 and b>0)
1. Product Property –
2. Quotient Property-
baab *
Example:Example:
10210*410*440
b
a
b
a
Example:Example:
2
3
4
3
4
3
![Page 5: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/5.jpg)
ExamplesExamples
1.
2.
3.
500 5*100 5*100 510
6*123 6*123 723 2*363
26*3 218
9
25
9
25
3
5
![Page 6: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/6.jpg)
Rationalizing the DenominatorRationalizing the Denominator
You CANNOT leave a radical in the denominator of a fraction!
(the numerator is OK)
Just multiply the top & bottom of the fraction by the radical to “rationalize” the
denominator.
![Page 7: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/7.jpg)
More Examples!More Examples!
1.
2.
3
25
3
25
3
5
3*
3*
9
35
3
35
Can’t have a tent in the Can’t have a tent in the basement!basement!
11
2
11
2
11*
11*
121
22
11
22
![Page 8: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/8.jpg)
Solving Quadratic EquationsSolving Quadratic Equations1. Solve. 3 - 5x2 = -9
-3 -3
-5x2 = -12
-5 -5
x2 = 5
12
5
122 x
5
152
5
15*4
25
60
5*5
5*12
5
12 x
2.Solve. 3(x-2)2=21 3 3
(x-2)2 = 7
7)2( 2 x
72 x
72 x
![Page 9: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/9.jpg)
More Examples!More Examples!
3. Solve. 4x2-6=42
+6 +6
4x2=48
4 4
x2 = 12
122 x
323*4 x
4. Solve. 4. Solve. 6)4(5
1 2 x
30)4( 2 x
30)4( 2 x
304 x
304 x
![Page 10: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/10.jpg)
Falling Objects!Falling Objects!
• Use h = -16t2 + h0
Height Height of the of the object object after it after it
has has fallenfallen
# of seconds # of seconds after the after the object is object is droppeddropped
Object’s Object’s initial initial heightheight
![Page 11: Solving quadratics with square roots](https://reader034.fdocuments.us/reader034/viewer/2022052122/55844aaad8b42adf748b480b/html5/thumbnails/11.jpg)
ExampleExample• 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?
1450160 2 t
0216 hth
2161450 t2625.90 t
2625.90 t
seconds 52.9t