Discriminant
y = x² + 2x + 1
An object is tossed straight up in the air and can be modeled by the equation h=−16t2 + 64t + 190, where t ≥ 0 is the time in seconds and h, is height in feet. Find the maximum height of the object.
hmax = 254 ft.
x2 - 4x + 5 = 0
x = 2 + i , 2 - i
x2 + 4x + 3 = 0
-c2 - 6c + 8 = 0
y = x² + 25
The height in feet of a bottle rocket is given by h(t)=160t −16t2, where t is the time in seconds. How long will it take for the rocket to return to the ground?
x2 + 6x + 12 = 0
x= -3 + i*sqrt(3), -3 - i*sqrt(3)
m2 − 5m − 14 = 0
2a2 - 6a - 3 = 0
x² - 5x - 34 = 0
You are standing on a bridge over a river, holding a rock 36 feet above the water. If you toss the rock up, with an initial velocity of 20 ft/s, how long until it hits the water?
t = 2.25 seconds
3d2 - 5d + 6 = 0
d = 5 + i*sqrt (47) / 6 , 5 - i*sqrt (47) / 6
2x2 + 3x − 20 = 0
14 - 3a2 = 2a
3x + 7 = -5x² - 4
You are armed with water balloons. You go to the roof of a 9-story building and look over the edge to the ground 90 feet below. You throw your water balloon straight down at 40 ft/s. How many seconds does it take for your balloon to hit your friend walking by who is 6 ft tall? (Round to the nearest 1000th)
5x2 - 2x + 2 = 3x2
x = 1 + i*sqrt(3) / 2 , 1 - i*sqrt(3) / 2
4b2 + 8b + 7 = 4
2m2 − 7m − 13 = −10
m = 7 + sqrt (73) / 4, 7 - sqrt (73) / 4
25x² - 15x - 64 = 5x - 10
A batter hits a baseball straight up when it is 3 feet off the ground with an initial vertical velocity of 80 feet per second:
A) If the ball is not caught, how long will it take for the ball to hit the ground?
B) What is the maximum height of the ball?
A.) t = 5.037
B.) hmax = 103 ft.
3t2 + 3t + 5 = -2t2 - 5t
t = -4 + 3i / 5 , -4 - 3i / 5
k2 − 31 − 2k = −6 −3k2 − 2k
k = 5/2 , -5/2
8n2 + 4n − 16 = −n2
n = -2 + 2sqrt(37) / 9 , -2 - 2sqrt(37) / 9