What are the key aspects of the graph of f(x) = x2 – b2, where b is a real number?
2 answers:
Answer with explanation:
The graph of the function is:
f(x)=x² -b²
Here, b is any Real Number.
f(x)=x² - k, where, k=b².
→y+k=x²
The given curve represents a Parabola having vertex at ,(0, -k) which can be Obtained by , putting, x=0 and, y+k=0→y= -k.
→The curve will open vertically Upwards having y axis as Line of Axis.
→It will cut, x axis at two points, if , k<0 and does not cuts the x axis , if k>0.
→Line, x=0, divides the Parabola into two equal Parts.
Given equation is .
Now we need to find about what are the key aspects of the graph of , where b is a real number.
We know that square of any number is always positive.
then must be a positive number.
So that means for any real number b, as the value of b increases then graph of f(x) shifts downward by units as compared to the graph of parent function
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Answer: 
Explanation: For a general binomial expansion,
, we know that the powers have to add up to the initial power. This means that the power of x and power of y have to add up to n. This is the binomial theorem.
To further demonstrate this, let's use:
We can easily expand this. Using Pascal's Triangle, we get:
As we progress along the expansion, we can see that in each term, the summation of each power remains constant, namely 4.
It doesn't matter what term the binomials are, because the power summation will never change.
This is why we can say that it is raised to the 12th power, and the binomial is:
(5x - 6y).
Thus, we get:
Explanation: For a general binomial expansion,
To further demonstrate this, let's use:
We can easily expand this. Using Pascal's Triangle, we get:
As we progress along the expansion, we can see that in each term, the summation of each power remains constant, namely 4.
It doesn't matter what term the binomials are, because the power summation will never change.
This is why we can say that it is raised to the 12th power, and the binomial is:
(5x - 6y).
Thus, we get:
Answer:
Step-by-step explanation:
We are given the following in the question:
We have to prove:
Proof:
we can write:
Hence, the two triangle are congruent by SAS congruency rule.
The attached image shows the two triangle.
