Features of Forms
What key features does FACTORED FORM tell us?
(list all)
x-intercepts
max/min
How do you go from factored form to standard form?
Multiply!!!
How do you go from standard form to VERTEX form?
complete the square!
given the expression: -16t2+ v0t + h0
what do v0 and h0 mean?
v0 = initial velocity
h0 = intitial height
Identify the key features of the following form:
x2 - 11x + 24
y-intercept: 24
minimum vertex
y = (x-1)(x+2)
y = x2 + x -2
Convert to factored form:
y = x2 + 6x + 5
y = (x+1)(x+5)
intitial height = 1.5 feet
intitial velocity = 25 ft/s
Identify the key features of the following form
-(x+2)(x-1)
x intercepts: x=-2 x=1
maximum vertex
Convert to standard form:
y = (3x+2)(x-4)
y = 3x2 - 10x - 8
convert to factored form:
y = x2 -12x + 35
y = (x-5)(x-7)
A rocket is launched in the air. the equation h(t) = -16t2 + 32t + 48 models its path. t is time in seconds, h(t) is feet.
What is the vertex? what do the values mean in context?
(1,64)
after 1 second reaches a max height of 64 feet
Identify the form AND the key features
-(x-4)2 + 3
vertex form
vertex: (4,3)
maximum
convert to standard form:
y = (x-3)2 - 4
y = x2 - 6x + 5
y = x2 - 6x + 5
y = (x-3)2 - 4
Ms. Arney threw a water balloon of a building. the equation h(t) = -16t2 + 35t + 42 models its path.
What was the maximum height?
When did the balloon hit the ground?
61.14 ft
3.05 seconds
Write the quadratic that has the following key features
x-intercepts: x=1 x=-3 , minimum vertex
(hint: write it in the form of the given key features!)
y = (x-1)(x+3)
convert to standard form:
y = 3(x+1)2 + 2
y = 3x2 + 6x + 5
Convert to Vertex form:
y= x2 + 12x - 12
What is the vertex?
y = (x+6)2 - 48
(-6, -48)
Thor is struck off a 102 meter building with an intial velocity of 89 m/s.
Write the equation. find the following.
What is his max height? at what time?
When does Thor land?
h(t) = -16t2 + 89t + 102
225.77 meters at 2.78 seconds
lands after 6.54 seconds