Sequences
An arithmetic sequence starts with 2, 4, 6, 8, ...
Find the next three terms.
10, 12, 14
Name the x-intercepts for y=(x-2)(x+6)
(2,0) and (-6,0)
What form is
y=(x-6)^2+2
Vertex Form!
(Now, what's the vertex?)
The height of a football can be measured by
h(t)=4+44t-16t^2
At what height was the football thrown?
4 feet
(we want the y-intercept, where t=0)
Find all solutions to:
x^2=25
x=5, x=-5
A geometric sequence starts 4, 12, 36, ...
What is the growth factor?
3
Name the x-intercepts for y = (x)(x - 2)
(0,0) and (2,0)
What form is
y=(x-9)(x+2)
Factored Form
Now, what are the x-intercepts?
The height of a football can be measured by
h(t)=4+44t-16t^2
What does the -16t^2 mean?
Gravity pulling the ball down!
Find all solutions to:
x^2-8=28
x=6, x=-6
An arithmetic sequence starts with 5 and has a rate of change of -3.
Find the next three terms of the sequence.
2, -1, -4
What is the y-intercept of
x^2+4x-10
(0, -10)
What form is
y=x^2+5x-6
Standard Form
Now, what is the y-intercept?
The height of a frisbee can be measured by
h(t)=(-16t-32)(t-8)
When did the frisbee hit the ground?
At time t=8
(we need the positive x-intercept)
Find all solutions to:
3x^2=27
x=3, x=-3
A sequence has the following recursive definition:
f(1)=4; f(n)=f(n-1)+7
Find the first 3 terms of the sequence.
4, 11, 18
What is the y-intercept of
x^2+5
(0, 5)
Convert this expression to standard form:
(x-2)(x+7)
x^2+5x-14
The height of a frisbee can be measured by
h(t)=(-16t-32)(t-8)
From what height was the frisbee thrown?
256 feet
(we need a y-intercept, set t=0)
Find all solutions to:
(x-3)^2=25
x=8, x=-2
A geometric sequence starts 81, 27, 9, ...
What is the growth factor?
1/3
Name the x-intercepts for y = (3x - 9)(x + 7)
(3, 0) and (-7, 0)
Convert this expression to standard form:
(x-4)^2
x^2-8x+16
The height of a frisbee can be measured by
h(t)=(-16t-32)(t-8)
When did the frisbee reach its highest point?
At time t=3.
(we need the x-coordinate of the vertex).
Find all solutions to:
(x+2)^2+9=25
x=2, x=-6