Introduction to Solving Quadratic Equations
description
Transcript of Introduction to Solving Quadratic Equations
![Page 1: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/1.jpg)
Introduction to Solving Quadratic Equations
Objective: Solve quadratic equations by taking square roots
![Page 2: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/2.jpg)
![Page 3: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/3.jpg)
9 12 115 44 114
![Page 4: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/4.jpg)
Square Roots
![Page 5: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/5.jpg)
Square Roots
![Page 6: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/6.jpg)
Example 1
![Page 7: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/7.jpg)
Example 1
![Page 8: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/8.jpg)
Try This
• Solve . Give exact solutions. Then approximate the solution to the nearest hundredth.
231195 2 x
![Page 9: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/9.jpg)
Try This
• Solve . Give exact solutions. Then approximate the solution to the nearest hundredth.
• We need to get x by itself.
• Add 19 to both sides• Divide by 5• Square root both sides
231195 2 x
07.7
50
50
2505
231195
2
2
2
x
x
x
x
x
![Page 10: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/10.jpg)
Example 2
![Page 11: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/11.jpg)
Example 2
![Page 12: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/12.jpg)
Try This
• Solve 49)2(4 2 x
![Page 13: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/13.jpg)
Try This
• Solve
• Divide by 4• Square root both sides• Subtract 2 from both sides• Solve
49)2(4 2 x
211
23
27
449
4492
2
,
2
2
)2(
49)2(4
x
x
x
x
x
![Page 14: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/14.jpg)
Example 3
• A rescue helicopter hovering 68 feet above a boat in distress drops a life raft. The height in feet of the raft above the water can be modeled by , where t is the time in seconds after it is dropped. After how many seconds will the raft dropped from the helicopter hit the water?
6816)( 2 tth
![Page 15: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/15.jpg)
Example 3
• A rescue helicopter hovering 68 feet above a boat in distress drops a life raft. The height in feet of the raft above the water can be modeled by , where t is the time in seconds after it is dropped. After how many seconds will the raft dropped from the helicopter hit the water?
• What are they asking us in terms of our equation?
6816)( 2 tth
![Page 16: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/16.jpg)
Example 3
• A rescue helicopter hovering 68 feet above a boat in distress drops a life raft. The height in feet of the raft above the water can be modeled by , where t is the time in seconds after it is dropped. After how many seconds will the raft dropped from the helicopter hit the water?
• What are they asking us in terms of our equation?• They are asking when is the height of the raft zero.
6816)( 2 tth
![Page 17: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/17.jpg)
Example 3
• A rescue helicopter hovering 68 feet above a boat in distress drops a life raft. The height in feet of the raft above the water can be modeled by , where t is the time in seconds after it is dropped. After how many seconds will the raft dropped from the helicopter hit the water?
6816)( 2 tth
1.2
1.2
6816
06816
16682
2
2
t
t
t
t
t
![Page 18: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/18.jpg)
![Page 19: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/19.jpg)
Pythagorean Theorem
![Page 20: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/20.jpg)
Example 4
![Page 21: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/21.jpg)
Example 4
![Page 22: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/22.jpg)
Example 4
![Page 23: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/23.jpg)
Try This
![Page 24: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/24.jpg)
Try This
12.8
66
25.7225.6
)5.8()5.2(
2
2
222
e
e
e
e
![Page 25: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/25.jpg)
Try This
1.8
66
25.7225.6
)5.8()5.2(
2
2
222
e
e
e
e
t
t
t
t
3.9
25.87
69.7556.11
)7.8()4.3(
2
2
222
![Page 26: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/26.jpg)
Example 5
![Page 27: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/27.jpg)
Example 5
![Page 28: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/28.jpg)
Example 5
![Page 29: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/29.jpg)
Example 5
![Page 30: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/30.jpg)
Try This
![Page 31: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/31.jpg)
Try This
6.690
476961)(
40000516961)(
719200)(
2
2
222
RQ
RQ
RQ
RQ
![Page 32: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/32.jpg)
Try This
6.690
476961)(
40000516961)(
719200)(
2
2
222
RQ
RQ
RQ
RQ
5.1897
3600464)(
400003640464)(
1908200)(
2
2
222
RP
RP
RP
RP
![Page 33: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/33.jpg)
Try This
6.690
476961)(
40000516961)(
719200)(
2
2
222
RQ
RQ
RQ
RQ
5.1897
3600464)(
400003640464)(
1908200)(
2
2
222
RP
RP
RP
RP
9.1206
6.6905.1897
PQ
PQ
RQRPPQ
![Page 34: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/34.jpg)
![Page 35: Introduction to Solving Quadratic Equations](https://reader036.fdocuments.us/reader036/viewer/2022062321/56813d7e550346895da75e27/html5/thumbnails/35.jpg)
Homework
• Pages 286-287• 15-43 odd