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Introduction to Solving Quadratic Equations
Objective: Solve quadratic equations by taking square roots
9 12 115 44 114
Square Roots
Square Roots
Example 1
Example 1
Try This
• Solve . Give exact solutions. Then approximate the solution to the nearest hundredth.
231195 2 x
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
Example 2
Example 2
Try This
• Solve 49)2(4 2 x
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
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
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
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
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
Pythagorean Theorem
Example 4
Example 4
Example 4
Try This
Try This
12.8
66
25.7225.6
)5.8()5.2(
2
2
222
e
e
e
e
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
Example 5
Example 5
Example 5
Example 5
Try This
Try This
6.690
476961)(
40000516961)(
719200)(
2
2
222
RQ
RQ
RQ
RQ
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
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
Homework
• Pages 286-287• 15-43 odd
