a. Use a graphing utility to graph y = 2 x 2 − 82 x + 720 in a standard viewing rectangle. What do you observe? b. Find the coordinates of vertex for the given quadratic function. c. The answer to part (b) is ( 205 , − 120.5 ) . Because the leading coefficient, 2, of the given Function is positive, the vertex is a minimum point on the graph. Use this fact to help Find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at x = 20.5 . the setting for x should extend past this, so try X min = 0 and X min = 30 . The selling for y should include (and probably go below) the y-coordinate of the graph's minimum y -value. so try Y min = 130 . Experiment with Y max until your utility shows the parabola's major features. d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.
a. Use a graphing utility to graph y = 2 x 2 − 82 x + 720 in a standard viewing rectangle. What do you observe? b. Find the coordinates of vertex for the given quadratic function. c. The answer to part (b) is ( 205 , − 120.5 ) . Because the leading coefficient, 2, of the given Function is positive, the vertex is a minimum point on the graph. Use this fact to help Find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at x = 20.5 . the setting for x should extend past this, so try X min = 0 and X min = 30 . The selling for y should include (and probably go below) the y-coordinate of the graph's minimum y -value. so try Y min = 130 . Experiment with Y max until your utility shows the parabola's major features. d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.
Solution Summary: The author explains how to graph the function y = 2x2-82x+720 using a graphing utility.
a. Use a graphing utility to graph
y
=
2
x
2
−
82
x
+
720
in a standard viewing rectangle. What do you observe?
b. Find the coordinates of vertex for the given quadratic function.
c. The answer to part (b) is
(
205
,
−
120.5
)
. Because the leading coefficient, 2, of the given Function is positive, the vertex is a minimum point on the graph. Use this fact to help Find a viewing rectangle that will give a relatively complete picture of the parabola. With an axis of symmetry at
x
=
20.5
. the setting for x should extend past this, so try
X
min
=
0
and
X
min
=
30
. The selling for y should include (and probably go below) the y-coordinate of the graph's minimum y-value. so try
Y
min
=
130
. Experiment with Y max until your utility shows the parabola's major features.
d. In general, explain how knowing the coordinates of a parabola's vertex can help determine a reasonable viewing rectangle on a graphing utility for obtaining a complete picture of the parabola.
Directions: Use the equation A = Pet to answer each question and be sure to show all your work.
1. If $5,000 is deposited in an account that receives 6.1% interest compounded continuously, how much money is in the
account after 6 years?
2. After how many years will an account have $12,000 if $6,000 is deposited, and the account receives 3.8% interest
compounded continuously?
3. Abigail wants to save $15,000 to buy a car in 7 years. If she deposits $10,000 into an account that receives 5.7% interest
compounded continuously, will she have enough money in 7 years?
4. Daniel deposits $8,000 into a continuously compounding interest account. After 18 years, there is $13,006.40 in the account.
What was the interest rate?
5. An account has $26,000 after 15 years. The account received 2.3% interest compounded continuously. How much was
deposited initially?
TRIANGLES
INDEPENDENT PRACTICE
ription Criangle write and cow
Using each picture or description of triangle write and solve an equation in ordering the
number of degrees in each angle
TRIANGLE
EQUATION & WORK
ANGLE MEASURES
A
B
-(7x-2)°
(4x)
(3x)°
(5x − 10)
C
(5x – 2)
(18x)
E
3.
G
4.
H
(16x)°
LL
2A=
2B=
ZE=
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