Algebraic Manipulation Worksheets - Algebra 2 Unit 5 (Chapter 4) - Buchanan Math Department Page 6
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11Worksheet 4
In each problem below there are two parabolas f(x) and g(x). Graph each parabola
on a separate grid. Label the line of symmetry and vertex of each. Using both
your graphs determine all the statements that apply to the pair of parabolas from
this list:
a) Both parabolas open the same direction
b) The parabolas have the same line of symmetry
c) The parabolas have the same vertex
d) Both parabolas have maximums
e) Both parabolas have minimums
f) The parabolas are the same width
g) The f(x) parabola is wider than the g(x) parabola
h) The g(x) parabola is wider than the f(x) parabola
1
2
2
1.
f(x) = –
(x – 4)
+ 3
g(x) = 2(x – 4)
+ 3
2
2
2
2.
f(x) = 3(x + 1)
– 2
g(x) = 3(x – 1)
+ 4
2
2
3.
f(x) = x
+ 6x + 8
g(x) = 3x
+ 6x – 9
2
2
4.
f(x) = –2x
– 4
g(x) = –2x
+ 4
1
2
2
5.
f(x) = 4(x – 2)
g(x) = –
(x – 2)
– 6
4
2
2
6.
f(x) = 2x
– 4x + 6
g(x) = –2x
+ 4x + 6
Solve the following word problems:
7.
The revenue, R, made selling phones at price, p, can be modeled by
−
5
2
R =
p
+ 500p
2
a) What price will maximize the companies revenue?
b) What is the maximum revenue?
8.
The revenue, R, made selling widgets at price, p, can be modeled by
2
R = -5p
+ 100p
a) What price will maximize the companies revenue?
b) What is the maximum revenue?
(Continued on next page)
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