Completing the Square
x2 − 12x + 11 = 0
11, 1
y = x2 + 14x – 14
(-7,-63)
y = x2 + 16x + 71
(-8,7)
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h, after t seconds is given by the equation h(t)= -16t2+128t
How long will it take the rocket to hit its maximum height?
4 seconds
2m2 + 2m − 12 = 0
2, -3
x2 + 6x + 8 = 0
-2, -4
y = x2 - 6x + 17
(3,8)
y = x2 − 2x − 5
(1,-6)
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h, after t seconds is given by the equation h(t)= -16t2+128t
If it took the rocket 4 seconds to reach the maximum height, what is the maximum height?
**Hint: They are giving you the t value, solve for y**
256 feet
x2 + 4x + 3 = 0
v2 + 6v − 59 = 0
-3 +/- square root of 17
y = x2 − 4x + 5
(2,1)
y = x2 + 10x + 33
(-5,8)
If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h, after t seconds is given by the equation h(t)= -16t2+128t
What was the starting height of the rocket?
0
There is no C value, the rocket started on the ground
b2 − 4b + 4 = 0
2
k2 − 12k + 23 = 0
6 +/- square root of 13
y = x2 − 4x + 2
(2,-2)
y + 6 = (x + 3) 2
(-3, -6)
A small independent motion picture company determines the profit P for producing n DVD copies of a recent release is P = -0.02n2 + 3.40n - 16. P is the profit in thousands of dollars and n is in thousands of units. a. How many DVDs should the company produce to maximize the profit?
n= 85
2x2 + 3x − 20 = 0
2.5, -4
r2 − 4r − 91 = 7
** WHEN YOU MOVE C TO THE RIGHT, YOU AREN'T ADDING IT TO '0'!!
2 +/- square root of 102
y = x2 − 16x + 70
(8,6)
x2 − 12x + y + 40
(6,-4)
You are trying to dunk a basketball. You need to jump 2.5 ft in the air to dunk the ball. The height that your feet are above the ground is given by the function h(t)= -16t2+12t
What is the maximum height your feet will be above the ground?
t= 0.375 (but it isn't asking time)
Plug in t and solve for the height -16(.375)2+12(.375) = 2.25
No, you're close, but you can't dunk the ball
2m2 − 7m − 13 = −10
7 +/- square root of 73 over 4