Quadratic Formula and Applications

The Quadratic Formula

2 cb

a

b

2

4a

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Video 1A (4:01)

Video 1B (3:53)

Video 2 (2:46)

Video 3 (0:32)

Video 4 (2:44)

Video 5 (0:25)

Rap 1 (2:13)

Rap 2 (3:19)

Rap 3 (2:52)

2 0 two unique real solub 4ac tions

2The Discrimina t b an 4 c

2 0 one real solution...doubleb 4a oc ro t2 0 cannot do yet (coming b 4ac soon)

22x 5x 2 0

25 4 2 2 9

2If is a perfect square, can facb 4ac tor.

2x 1 x 2 0

1x , x 2

2

2x 6x 9 0

26 4 1 9 0

x 3 x 3 0

x 3 double root

23x 5x 1 0

25 4 3 1 37 Yes

x6

35 7

22x 3x 4 0

a) Does the equation yield two unique real solutions?b) If yes to part (a), find the two solutions.

23 4 2 4 23 No

2x 6x 2 0

26 4 1 2 28 Yes

6x

2

28

6 2 7

2

3 7

Try these four:24x 2x 6 0 2x 5x 1 0

2 22x 2x 7 x 2x 2 3 2x 3x x 0

25 4 1 1 29 yes

5x

2

29

22 4 4 6 100

factorable

22 2x x 3 0

2 2x 3 x 1 0 3

x , x 12

2x 4x 5 0 24 4 1 5 4 no

2x x 3x 1 0

23 4 1 1 13 yes

3x 0, x

2

13

x 0 (double root), NF

2 23x 2x x 4 0

4 3 26x 3x 12x 0

4 3 4 3 27x 6x x 3x 12x

From Factoring Day 3:

Now becomes…

2 23x 2x x 4 0

4 3 26x 3x 12x 0

4 3 4 3 27x 6x x 3x 12x

21 4 2 4 33 Yes

1 33x 0 double root , x

4

CALCULATOR REQUIRED

A courtyard measuring 12 feet by 16 feet needs a pedestrian walkway all around it. This walkway would increase the total area to 285 square feet. What will be the width of the walkway?

12

16xx

x

x

16 2x 12 2x 285

1.5 or 1.5 feet

CALCULATOR REQUIRED

You are to take a square piece of cardboard, cut three-inch squares from each corner, and fold it into a box which has a volume of 71 cubic inches. What are the dimensions of the smallest square piece of cardboard which can be purchased to create such a box? Assume square pieces of cardboard are sold in whole inch dimensions only.

33

3

3

x – 6

x – 6

3 x 6 x 6 71 11” x 11”

CALCULATOR REQUIRED

Find all possible sets of three consecutive integers such that four times the sum of all three is two times the product of the larger two.

x x 1 x 2

4 x x 1 x 2 2 x 1 x 2

-1, 0, 14, 5, 6