Introduction to Solving Quadratic Equations

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