Quadratic Word Problems WS 2 Solutions

#1 10 inches

#2

#3

#4

#5

#6

15 cm by 7 cm

a. 156.25 ft b. 6.25 sec c. 0.55 & 5.70 sec

72 units

96 cm

Height is 5.25 m or 5 m and 25 cmDistance is 3.79 meters or 3 m and 79 cm

About 10 inches

#1

2x + 15

2x + 20

(2x +15)(2x +20) −(15)(20) =60 x =

−35 ± 35 2 −4 • 2 • −30

2 • 2

4x2 + 70x + 300 −300 =60

4x2 + 70x −60 =0

2x2 + 35x −30 =0

x =

−35 ± 1465

4≈0.8188

0.8188 ft x 12 in/ft

#2

The dimensions of the rectangle are 15 cm by 7 cm

Perimeter = 44 cmArea = 105 sq. cm

Width = W

Length = L

2L + 2W = 44

L + W = 22

L = 22 - W

(L)(W) = 105

(22 - W)(W) = 105

22W – W2 = 105

W2 – 22W + 105 = 0

(W - 15)(W - 7) = 105

#3a h = -16t2 + 100t

t =−

b

2a=−100

−32=25

8

h=−16

25

8

⎛

⎝⎜

⎞

⎠⎟

2

+10025

8

⎛

⎝⎜

⎞

⎠⎟

First find Axis of Symmetry

Plug it in to get the vertexSolving for h will give the maximum point (or highest point)

h=−16

625

64

⎛

⎝⎜

⎞

⎠⎟ +25

25

2

⎛

⎝⎜

⎞

⎠⎟

h=−

625

4+625

2=625

4=156.25

#3b

Why does this work?

h = -16t2 + 100t

25

8• 2 =

25

4=6

1

4

Alternate solution

0 = -16t2 + 100t

0 = -4t(4t – 25)

t = 0 or 6.25

Two ways to solve …

#3c h = -16t2 + 100t

x =

50 ± 2500 −4g8g25

2(8)

50 = -16t2 + 100t

16t2 - 100t + 50 = 0

8t2 - 50t + 25 = 0

x =

50 ± 1700

16=50 ±10 17

16 ≈0.55 or 5.70

#4

x

x + 6

x

x + 9

(x)(x) =

1

2x + 6( ) x + 9( )

x2 =

1

2x2 +15x + 54( )

2x2 =x2 +15x + 54

x2 −15x −54 =0

(x −18)(x + 3) =0

x =18

Square's perimeter = 72 units

Volume = L x W x H

Width = w

Length = 3w

512 = (3w - 4)(w - 4)(2)

w - 4 3w - 4

256 = (3w - 4)(w – 4)

256 = 3w2 – 16w + 16

0 = 3w2 – 16w - 240

0 = (w – 12)(3w + 20)

Width = 12 cm

Perimeter = 96 cm

3 meters

Maximum height (at vertex)

height when I hit the water?

Distance from board when entering water?

Mr. Lomas (at least the way I remember me) ….

y =−x 2 + 3x + 3

#6

y =−x 2 + 3x + 3

x =

−b

2a=3

2

y =−

3

2

⎛

⎝⎜

⎞

⎠⎟

2

+ 33

2

⎛

⎝⎜

⎞

⎠⎟ + 3

y =−

9

4+9

2+ 3

y =−

9

4+18

4+12

4=21

4=5.25

Maximum height of 525 cm

0 =−x 2 + 3x + 3

x2 −3x −3 =0

x =3 ± −3( )

2

−4 1( ) −3( )

2 1( )

x =

3 ± 21

2≈3.79 meters

#7Equation: y = x2 - 10x + 15 Direct: UpWidth: StandardL of S: x = 5Vertex: (5, -10)y-int: (0, 15)

Roots: 5± 10

#8Equation: y = -2x2 + 8 Direct: DownWidth: NarrowL of S: x = 0Vertex: (0, 8)y-int: (0, 8)Roots: 2 or -2

#9Equation: y = (1/4)x2 - 2x - 5 Direct: UpWidth: WideL of S: x = 4Vertex: (4, -9)y-int: (0, -5)Roots: 10 or -2