Download Algebra 2 Warm-ups thru sept 30

Algebra 2
Unit 1: Warm ups
Doering
Wednesday 9/9
Expand:
1.) (x + 3)2
2.) (x – y)2
3.) (2x + h)2
Thursday 9/10
• Rationalize the denominator
1
3
6
10
5
3
4
3 2
Monday 9/13
Warm-ups (in “work” notes)
• Are the following relations
also functions? Why or
why not?
• Evaluate given the
following:
f ( x)  5  2 x
g ( x)  x 2  2 x
a.) {(1,5), (5,1), (4, 4), (5, 4)}
b.) y = 2x +3
c.) y = x
d.) y = 3
e.) x = 2
f (3)
g (4)
f ( x  5)
g ( a  b)
3 g (1)  2 f (2)
Tuesday 9/14
Warm-ups (in “work” notes)
d  ( x2  x1 ) 2  ( y2  y1 ) 2
 x2  x1 y2  y1 
,


2 
 2
• Evaluate given the
following:
f ( x)  5  2 x
g ( x)  x 2  2 x
•
Given A (2, – 4) and B (– 6, 2)
•
Find the distance between points
A and B
•
Find the midpoint between points
A and B
f ( x)  g ( x)
f ( x)  2 g ( x)
f ( x) g ( x)
Wednesday 9/15
Warm-ups (in “work” notes)
Given:
{(1, 2),(2, 3),(3, 2),(4, 0),(5,2)}
• Evaluate given the
following:
f ( x)  5  2 x
a.) Express the relation using a
mapping diagram
b.) Identify the domain
g ( x)  x 2  2 x
f ( g ( x))
c.) Identify the range
g ( f ( x))
d.) Is the relation also a function?
Why or why not?
f ( f ( x))
Thursday 9/17
Warm-ups (in “work” notes)
Let (2, 12) and (4, – 2) be the end points of a circle.
• Find the equation of the circle
• Find the center and radius
• Sketch the circle
• Find the equation of a line that is tangent to the circle
Monday 9/20
Warm-ups (in “work” notes)
• Solve for x:
1.)5  ( x  2)  3  x
2.)3( x  1)  3 x  5
2
3.)4  x  6
3
4.)5  2(3  x)  30
Tuesday 9/21
Warm-ups (in “work” notes)
1.) Find the x-intercept and y-intercept for
the line: 3x + 2y = 24
2.) The intercepts of a line are (– 3, 0) and
(0, 2). Find the equation of the line.
3.) Where do y = – 4 and x = 7 intersect?
Wednesday 9/22
Warm-ups (in “work” notes)
Given:
Solve for x:
f ( x)  10  3x
g ( x)  x  2 x  3
2
Find:
f ( g ( x))
g ( f ( x))
1 x 2 7
  
3 4 5  8
2x  3  5
Thursday 9/23
Warm-ups (in “work” notes)
1.) Given:
f(x) = 12 – 5x
2.) Find the x-intercept
and y-intercept for the
line: 4x – 3y = 24
Find:
a.) f(– 4)
b.) f(x – 7)
c.) f(x + 3a)
3.) Sketch the line in
question #2
Friday 9/24
Warm-ups (in “work” notes)
1.) Write equation of a line that passes
through (2, 1) and (4, 9).
2.) Find equation of a line that passes
through (2, 1) and is perpendicular to
3x + 2y = 24.
3.) Solve and graph solution
2x  5  3
Monday 9/27
Warm-ups (in “work” notes)
• Solve
2 x  4 y  13


4 x  5 y  8 
• Given
f ( x)  x 2  4
• Evaluate
f ( f ( x))
Tuesday 9/28
Warm-ups (in “work” notes)
• Solve
1.)
x y 6




 x  2 
3.)
2.)
9 2
7
3

x 2
5 3
6
2
 y  5



x  3

2 x  y  13


Wednesday 9/29
Warm-ups (in “work” notes)
Solve
1.) Write an equation of a line that passes
through (3, 7) and is parallel to
3x – 4y = 17
Thursday 9/30
Warm-ups (in “work” notes)
You want to burn 380 calories during 40
minutes of exercise. You burn 8 calories
per minute cycling and 12 calories per
minute swimming. How long should you
spend during each activity?