The graphs below have the same shape. What is the equation of the blue
graph?
5
f(x) = x
W
Na
g(x) = 2
g(x) = -
O A. g(x) = (x - 4)2 + 1
O B. g(x) = (x+4)2 - 1
O c. g(x) = (x - 4)2 - 1
O D. g(x) = (x+4)2 + 1

Answer:

If the attached graph is the one you mean, the answer is g(x) = (x-4)^2 + 1

The equation of the blue graph is,

⇒ g (x) = (x - 4)² + 1

Given that;

The given function is,

⇒ f (x) = x²

Since, It is given that both graph has same shape it means the equation of blue graph is in the form of;

⇒ g (x) = (x - h)² + k

Where, (h,k) is the vertex of the parabola.

Hence, From the given graph it is noticed that vertex of blue parabola is (4,1),

Therefore, the equation of parabola is,

⇒  g (x) = (x - 4)² + 1

Thus, The equation of the blue graph is,

⇒ g (x) = (x - 4)² + 1

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You’ve probably heard police officers on television repeat the same line every single time they arrest someone: “You have the right to remain silent.” Have you ever wondered why they always say this? As it turns out, all police officers in the country are required by law to say these words, which are called “Miranda Rights.” They are named after a famous court case from 1966, Miranda v. Arizona.

THE CASE
In 1966, an Arizona man named Ernesto Miranda was accused of kidnapping and assaulting a teenage girl. After a few hours of questioning, he confessed his guilt to a police officer. Later, during his trial, the prosecution
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The case went all the way to the Supreme Court. The case related to the Constitution, because the 5th Amendment to the Constitution gives everyone the right to stay quiet when they are asked to confess a crime. Miranda’s lawyers argued that Miranda did not know about this right, and therefore his testimony
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THE RESULT
Since Miranda did not know about his 5th Amendment rights, his confession could not be used against him, and the Supreme Court ruled in his favor. The official court decision was over 60 pages long, but Chief Justice Earl Warren read the whole thing out loud for the court. It had two parts:

First, after the police arrest someone, they have to tell that person that they have the right to remain silent, just as it is stated in the 5th Amendment.

Second, the police also have to tell that person they have the right to use a lawyer in the trial and any time prior to that, and that if they cannot afford a lawyer, the government will provide them with one. These rights are both found in the 6th Amendment.

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MIRANDA RIGHTS TODAY
The basic wording might sound familiar. “You have the right to remain silent. Anything you say can and will be used against you in a court of law. You have the right to an attorney. If you cannot afford an attorney, one will be appointed to you. Do you understand these rights as I have read them to you?” However, there are actually over 945 versions of the Miranda Rights! Every state and county can have its own wording.

Not only that, but the Miranda Rights also have to be translated into many different languages, in case the police arrest someone who does not speak English. There are also simplified versions, because it is important for minors
and the mentally disabled or mentally ill to understand their rights as well.

As it turns out, even 945 versions are not enough to make sure everyone understands what their rights really are. Some researchers have analyzed the wording of Miranda Rights from all over the country, and most versions are too complex for everyone to understand. Some are so complex, they are at the same reading level as a college accounting textbook!

It is extremely important that everyone can understand their right to remain silent and their right to be represented by a lawyer. The law says that, in order to use a suspect’s own confession against him, the court has to prove that the police read them their rights, they completely understood their rights, and that they chose to ignore those rights intentionally. The Constitution gave us these rights for a reason; make sure you understand them!

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