Algebra 2 — Chapter 2 Day #2
Homework Graphing Parabolas Quickly (2.1.3)
Name
L-8. Consider the sequence with a first term of 256, followed by 64, 16, ...
a. Write the next three terms of this sequence, then find an equation for the sequence.
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b. If you were to keep writing out more and more terms of the sequence, what would happen to the terms?
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c. Sketch a graph of the sequence. Should you connect the
points? Why or why not?
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d. What happens to the points as you go farther to the right?
closet c).-4
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e. What is the domain of the sequence?
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f. What is the domain of the function with the same equation as this sequence?
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Algebra 2 — Chapter 2 Day #2
Homework Graphing Parabolas Quickly (2.1.3)
Name
2-19. Simplify each of the following expressions. Be sure that your answer has no negative or fractional
exponents,
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c16X242
a. (1?
c. (2X) 2
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2-35. Solve each of the following equations without using the Quadratic Formula.
c. 2x 2 — 14x + 3 = 3
a. y 2 — 6y = 0
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lie (t)
=U
hc7- — x
()
D
2-x( x- 7) '0
e. What do these two equations have in common that causes them to have zero as a solution?
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2-36. Find the vertex of each of the following parabolas by averaging the x-intercepts. Then write each equation
in graphing form.
b. y = (x + 2)(x — 6)
a. y = (x — 3)(x — 11)
X= 3
x \
A= - 2
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0- =
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Algebra 2 — Chapter 2 Day #2
Homework Graphing Parabolas Quickly (2.1.3)
440
c. y = x 2 — 14x + 40
Name
d. y = (x — 2)2 — 1
(x --( 0)(x - Li)
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2-37a. Did you need to average the x-intercepts to find the vertex in part (d) of the preceding problem?
What are the coordinates of the vertex for part (d)?
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2-38. Scientists can estimate the increase in carbon dioxide in the atmosphere by measuring increases in carbon
emissions. In 1998 the annual carbon emission was about eight gigatons (a gigaton is a billion metric
tons). Over the last several years, annual carbon emission has been increasing by about one percent.
a. At this rate, how much carbon was predicted to be emitted in 2010?
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b. Write a function, C(x), to represent the amount of carbon emitted in any year starting with the year 2000.
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Algebra 2 - Chapter 2 Day #2
Homework Graphing Parabolas Quickly (2.1.3)
2-39. Make predictions about how many times the graph of each equation below will touch the x-axis. You may
first want to rewrite some of the equations in a more useful folio.
a. y = (x - 2)(x - 3)
b. y =
+ 1)2
ono, eitrY ■s--\
I
d. y = x 2 + 7x + 10
c. y =x 2 + 6x + 9
(3-
r-
(x+-5)CX+
()C it nCX
)0=
01(U '\)ri`sz
5-
X. c"-re1/4-1,5
rtuo o
e. y =
Cy\ .; L-1)CY.
ll
f. y = -x 2 - 4x - 4
+ 6x + 8
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A- re--)
Nt -/- LiN -4-(4)
- ( X 4 2-)0(
CX- 22))-
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two ATCY\-6
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g. Check your predictions with your calculator. Write a clear explanation describing how you can tell
whether the graph of a parabola will touch the x-axis at only one point.
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ver-ux
U3N 1
1
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2-40. Simplify each of the following expressions. Be sure that your answer has no negative or fractional
exponents.
a. 64 3
b. (4x 2 y 5 )
0,-1
351-
/(0)(9 y I °
c. (2x2y-2)(3xy5)
.2)it • 3
5
)a