All interior angles are congruent True or False
1 answer:
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Answer:
-9, 15
Step-by-step explanation:
Subtract 7 and multiply by 4
1/4 |2x-6| +7 = 13
1/4 |2x -6| = 6
|2x -6| = 24
2x -6 = ± 24
2x = 6 ±24
x = 3 ±12
x = -9, 15
_____
For graphing purposes, it is often convenient to rewrite the equation so the solutions are where the function is zero. Here, we can do that by subtracting 13 from the equation.
(1/4 |2x -6| +7) -13 = 0
Short Answer: y = 3*cos(2x) + 1
Remark
This is not part of the answer, but it will help you to see what is going on. Begin by shifting the cos graph 1 unit down. That will that the cos has a minimum of -3 and a max of + 3
What that tells you is the part of the equation is
y = 3*cos(x)
Step One
Show that the graph is of something that resembles y = 3*cos(x)
the test way to check this is to put in 0 for x
3*cos(0) = 3*1 = 3. But why is it 4 and -2 instead of 3 and -3.
Step Two
Show how the graph is shifted up one space.
y movement is always recorded behind how the variable is determined.
So if the graph is shifting up one, you should do this.
y = 3cos(x) + 1
Step Three
The graph seems to be starting over at n*pi rather than n*2pi. How do we adjust for that?
There are 2 choices. Either there is a 4 in front of the x or there is a 1/2 in front of the x. Before just telling you, consider the graph below.
Violet is 3*cos(1/2 x)
Blue is 3*cos (x)
orange is 3*cos(2*x)
You want the graph that starts over again at x = 3.14 rather than at x = 6.28
The one that starts over at y = 3*cos(2x)
The rule is that if you want to compress a trigonometric function, use a constant such that a > 1 y = 3*cos(a*x). It is the a I'm trying to explain.
Step 4
Is there a phase shift?
No. If there was cos(x) would not have a maximum at x = 0
Answer y = 3*cos(2x) + 1
Remark
This is not part of the answer, but it will help you to see what is going on. Begin by shifting the cos graph 1 unit down. That will that the cos has a minimum of -3 and a max of + 3
What that tells you is the part of the equation is
y = 3*cos(x)
Step One
Show that the graph is of something that resembles y = 3*cos(x)
the test way to check this is to put in 0 for x
3*cos(0) = 3*1 = 3. But why is it 4 and -2 instead of 3 and -3.
Step Two
Show how the graph is shifted up one space.
y movement is always recorded behind how the variable is determined.
So if the graph is shifting up one, you should do this.
y = 3cos(x) + 1
Step Three
The graph seems to be starting over at n*pi rather than n*2pi. How do we adjust for that?
There are 2 choices. Either there is a 4 in front of the x or there is a 1/2 in front of the x. Before just telling you, consider the graph below.
Violet is 3*cos(1/2 x)
Blue is 3*cos (x)
orange is 3*cos(2*x)
You want the graph that starts over again at x = 3.14 rather than at x = 6.28
The one that starts over at y = 3*cos(2x)
The rule is that if you want to compress a trigonometric function, use a constant such that a > 1 y = 3*cos(a*x). It is the a I'm trying to explain.
Step 4
Is there a phase shift?
No. If there was cos(x) would not have a maximum at x = 0
Answer y = 3*cos(2x) + 1