"The Basics"
What do you plug in for t to find out how high off the ground an object starts?
0
Why do we "ignore" the negative root in all of our answers?
Because the negative root indicates a negative time. Negative times do not make sense!
What equation do we use to find the x-value of the vertex? (the axis of symmetry)
x=(-b)/(2a)
A ball is launched from a platform. The equation for the ball's path is represented by
h = -16t^2+64t+24
Where h is the height in feet, and t is the time in seconds. What is the height of the platform?
24 feet
How many places to the right of the decimal is the hundredth place?
2
Setting an equation equal to zero will help you find the _____ of that equation?
Roots, zeroes, solutions, or x-intercepts
When a cannonball is fired, it follows the path
h=-16t^2+128t
Where h is the height in feet and t is the time in seconds. When will the cannonball hit the ground?
Factor OR use calculator!
t=8 seconds
A toy rocket is launched from a platform. The equation for the rocket's path is represented by
h = -16t^2+64t+80
Where h is the height in feet, and t is the time in seconds. ALGEBRAICALLY, when does the rocket reach its highest point?
x=(-b)/(2a)
x=-64/(2(-16))
x=2
2 seconds
A fireworks display is conducted in a park. The fireworks follow the path
h=-15t^2+75t
Where h is the height in feet, and t is the time in seconds. At what height are the fireworks launched from?
0 feet or the ground
Round 6.9812 to the nearest hundredth
6.98
At the vertex, the y-value tells you what information about the object's path?
The max height of the object or how high the object gets
A boat drops its anchor into the lake. The anchor follows the path
h=-4t^2+256
where h is the height in feet and t is the time in seconds. When will the anchor hit the bottom of the sea?
Factor OR use calculator!
t=8 seconds
A football is thrown from a balcony. The equation for the football's path is represented by
h = -(1/2)t^2+6t
Where h is the height in feet, and t is the time in seconds. When does the football reach its highest point?
Use axis of symmetry or use calculator!
t=6 seconds
A coin is dropped out of a third story window. The coin's path is represented by
h=-16t^2+49
Where h is the height in feet, and t is the time in seconds. ALGEBRAICALLY, show when the coin hits the ground.
-16t^2+49=0
-16t^2=-49
t^2=49/16
sqrt(t^2)=sqrt(49)/sqrt(16)
t=pm7/4
1.75 seconds
Round 5.753 to the nearest tenth
5.8
At the y-intercept, the y-value tells you what information about the object's path?
How high off the ground the object starts, or initial height
A soccer ball is kicked from the ground. It follows the path
h=-16t^2+90t
where h is the height in feet and t is the time in seconds. How many seconds will it take for the soccer ball to reach the ground? Round to the nearest tenth of a second.
Factor OR use calculator!
t=5.6 seconds
A toy rocket is launched from the top of a hill. The equation for the rocket's path is represented by
h = -16t^2+32t+48
Where h is the height in feet, and t is the time in seconds. What is the rocket's maximum height?
Axis of symmetry equation, then plug answer into equation OR use calculator!
h=64 feet
A rock is thrown off a cliff into the sea. The rock's path is represented by
h=-16t^2+64t+80
Where h is the height in feet, and t is the time in seconds. ALGEBRAICALLY, show when the rock hits the sea.
-16t^2+64t+80=0
-16(t^2-4t-5)=0
t^2-4t-5=0
(t-5)(t+1)=0
t=5, t=-1
5 seconds
Round 4.509 to the nearest whole number
5
At the vertex, the x-value tells you what information about the object's path?
WHEN or what time the object is at its max height
A cliff diver jumps into the water following the path
h=-16t^2+16t+480
Where h is the height in feet, and t is the time in seconds. ALGEBRAICALLY, show when the cliff diver hits the water.
-16t^2+64t+80=0
-16(t^2-t-30)=0
(t-6)(t+5)=0
t=6, t=-5
6 seconds
A toy rocket is launched from a platform. The equation for the rocket's path is represented by
h = -16t^2+64t+24
Where h is the height in feet, and t is the time in seconds. ALGEBRAICALLY, what is the rocket's maximum height?
x=(-b)/(2a)
x=-64/(2(-16))
x=2
2 seconds is when the rocket reaches max height.
*plug 2 into the equation*
88 feet
An astronaut on the moon throws a baseball. The baseball's path is represented by
h=-4.9t^2+10t+3
Where h is the height in feet, and t is the time in seconds. ALGEBRAICALLY, show when the baseball hits the ground. Round to the nearest hundredth of a second
a=-4.9,b=10,c=3
x=(-(-4.9)pmsqrt((10)^2-4(-4.9)(3)))/(2(-4.9)
x=-0.2654,2.306
2.31 seconds
For the number below, which digit is in the ten-thousandth place?
328.79145
4