What is the vertex of the graph of f(x) = |x 3| 7? (3, 7) (7, 3) (–3, 7) (7, –3).
2 answers:
The vertex of the given modulus function is (3,-7).
Given information:
The given modulus function is,
It is required to find the vertex of the given function.
<h3>What is the vertex of a modulus function?</h3>Modulus function is in the shape of V. The notch of V is the vertex of the function.
The given function can be defined as,
From the above function, it can be concluded that the vertex of the function should be (3,-7). Also shown in the attached image.
See the attached image.
Therefore, the vertex of the given modulus function is (3,-7).
For more details about modulus function, refer to the link:
The vertex of the graph of f(x) is (-3, 7).
<h2>Given that</h2>Graph;
What is the vertex of the graph of f(x)?
According to the question
The standard form of the absolute value function is;
Where h and k are the vertexes of the function.
Graph;
Converting the equation into the standard form the absolute value function;
On comparing with the standard absolute value function the vertices of the graph f(x).
h = -3 and k = 7
Hence, the vertex of the graph of f(x) is (-3, 7).
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Answer:
Step-by-step explanation:
This is a homogeneous linear equation. So, assume a solution will be proportional to:
Now, substitute into the differential equation:
Using the characteristic equation:
Factor out
Where:
Therefore the zeros must come from the polynomial:
Solving for :
These roots give the next solutions:
Where and
are arbitrary constants. Now, the general solution is the sum of the previous solutions:
Using Euler's identity:
Redefine:
Since these are arbitrary constants
Now, let's find its derivative in order to find and
Evaluating :
Evaluating :
Finally, the solution is given by: