Operations w/ Imaginary #s
(4 + 3i) + (2 + 6i)
6 + 9i
x2 = -25
x = 5i, x = -5i
Braden jumped off a cliff and into the ocean. His height h after time t seconds is given below. Write an equation for the curve of best fit.
t h
0 480
1 482
2 452
3 390
4 296
y=-16x2 + 18x + 480
Jeremy kicks a football. Its height in feet is given by h(t)= -16t2+16t where t represents the time in seconds after the kick.
How high was the ball as it was being kicked?
0 feet
x2 - 8x + 20 = 0
x = 4+2i, x = 4-2i
(8 + 3i)(8 - 3i)
73
5x2 + 20 = 0
x = 2i, x = -2i
Sarah is standing on a bridge that stands 50 feet above the water. She tosses a coin into the water. The heigh, h, of the coin at time t seconds in given in the table below. Write an equation for the curve of best fit.
h t
0 50
0.5 64
1 70
1.5 68
2 58
y = -16x2 +36x + 50
At local pretzel shop, the Knot, the amount of profit, y, made by selling pretzels is given by the equation:
y= -x2+84x+95.
What is the maximum number of pretzels to be sold (at the maximum monthly revenue)?
42 pretzels
x2 - 4x + 13 = 0
x = 2+3i, x = 2-3i
(4 +3i)(2 - 5i)
23 - 14i
2x2 + 32 = 0
x = 4i, x = -4i
A study compared the speed in miles per hour, x, and the average fuel economy in miles per gallon, y, for cars. The results are shown below. Write an equation for the curve of best fit.
x y
20 25.2
30 28.5
40 30.1
50 30.4
60 27.8
70 25.0
y = -.0084x2 + .752x + 13.55
Penelope throws a ball off the top of a building. The initial velocity of the ball is 30 feet per second.
The throw is modeled by h(t)= -16t2+30t+350.
How high is the ball when it has travelled for 4 seconds?
214 feet
x2 + 6x + 13 = 0
x = -3+2i, x = -3-2i
Simplify: i 75
-i
x2 - 5x - 24 = 0
x = 8, -3
The table below shows the sale price, p, of a house in Norfolk, Virginia in thousands of dollars during various years, t. Write an equation for the curve of best fit.
t p
2005 158
2006 145
2007 132
2008 130
2009 138
2010 142
y = 3.02x2 - 12119.64x + 12168173.86
or
y = 3.02x2 - 18.03x + 158.25
Jeremy kicks a football. Its height in feet is given by h(t)= -16t2+16t where t represents the time in seconds after the kick.
How long does it take for the ball to hit the ground?
1 second
3x2 - 18x + 219 = 0
x = 3+8i, x = 3-8i
Simplify: i 34
-1
x2 + 6x - 36 = 4
x = -10 , 4
What is the tallest manmade tower in the world?
Burj Khalifa
A rocket is launched from a tower. The height of the rocket can be modeled by h(t)= -16t2+161t+69 where h(t) represents the height of the rocket after t seconds.
After how many seconds is the rocket at a height of 200 feet?
at both 0.89 seconds and 9.17 seconds
2x2 - 12x + 116 = 0
x = 3+7i, x = 3-7i