5.2 Solving Quadratic Equations

Warm-up (IN)

CSAP Constructed Response

Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve problems involving right triangles.

Notes

Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve problems involving right triangles.

Properties of Square roots** Product property - ab ba

32

216 4 2

** Quotient property - b

a

b

a

9

4

9

4

3

2

Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve problems involving right triangles.

EX 1 – Solve 103237 a. 2 x27x 1262x 18 x 29 23 or 24.4

289546 b. 2 x

SADMEP!

25x 64

289

5x 17

8

x 8

175

or

x 8

17 5

8

23

8

57

Try t his p. 282 (middle and bottom)

Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve problems involving right triangles.

EX 2 – A helicopter 85 ft above a designated area drops a boxes of food to a disaster area. The height of the box above the ground can be modeled by , where t is the time in seconds after it has been released. After how many seconds will it hit the ground?

8516 2 tth

85160 2 t21685 t

2t4

17

2.3sect

Pythagorean Theorem!

Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve problems involving right triangles.

In a right , the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.

a

b

c22 2a cb

EX 3 – Find the unknown length

a. A B

5.3

8.4

b

C

28.4 23.5 2b56.70 09.28 2b

65.98 2b93.9 2b

b. J K

2.8

1.9

k

L

29.1 2k 28.261.3 2k 84.7

2k 23.4k 06.2

Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve problems involving right triangles.

Learning Objective: To solve quadratic equations by taking square roots and to use the Pythagorean Theorem to solve problems involving right triangles.

EX 4 – What must be the length of QS so that it contacts the ground halfway between the base of the tower and the point where PS contacts the ground?

S

P

75 ft106 ft

Q R

275 2PR 21065626 2PR 11236

2PR 5611PR 91.74 PRQR

2

1

45.37QR245.37 275 2SQ5625 2SQ

ft83.83 SQ

HW – p. 287

#21-43 odd,

51-54

Out – Describe the procedure you would use to solve

Summary – So, I was thinking…

POW!!

1235 2 x