Amplitude:4
Equation of Midline: 2
Period of function:3
Function shifted left:0.5
Function shifted up: 2
There is a multiple zero at 0 (which means that it touches there), and there are single zeros at -2 and 2 (which means that they cross). There is also 2 imaginary zeros at i and -i.
You can find this by factoring. Start by pulling out the greatest common factor, which in this case is -x^2.
-x^6 + 3x^4 + 4x^2
-x^2(x^4 - 3x^2 - 4)
Now we can factor the inside of the parenthesis. You do this by finding factors of the last number that add up to the middle number.
-x^2(x^4 - 3x^2 - 4)
-x^2(x^2 - 4)(x^2 + 1)
Now we can use the factors of two perfect squares rule to factor the middle parenthesis.
-x^2(x^2 - 4)(x^2 + 1)
-x^2(x - 2)(x + 2)(x^2 + 1)
We would also want to split the term in the front.
-x^2(x - 2)(x + 2)(x^2 + 1)
(x)(-x)(x - 2)(x + 2)(x^2 + 1)
Now we would set each portion equal to 0 and solve.
First root
x = 0 ---> no work needed
Second root
-x = 0 ---> divide by -1
x = 0
Third root
x - 2 = 0
x = 2
Forth root
x + 2 = 0
x = -2
Fifth and Sixth roots
x^2 + 1 = 0
x^2 = -1
x = +/- ![\sqrt{-1}](https://tex.z-dn.net/?f=%20%5Csqrt%7B-1%7D%20%20)
x = +/- i
Answer:
The ratio between won and lost is ![\frac{7}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B4%7D)
Step-by-step explanation:
<u><em>The question in English is</em></u>
A table tennis team won 21 games and lost 12 games, what is the ratio between won and lost?
Let
x ------> the number of games won
y -----> the number of games lost
we have
![x=21\ games](https://tex.z-dn.net/?f=x%3D21%5C%20games)
![y=12\ games](https://tex.z-dn.net/?f=y%3D12%5C%20games)
we know that
To find the ratio divide the number of games won by the number of games lost
so
![\frac{x}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7By%7D)
substitute the values
![\frac{21}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7B12%7D)
Simplify
![\frac{7}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B4%7D)
You can show it 4 ways by rotating the paper and if that is not an option, then the answer is 2.
The error is that 9 shouldnt be written as nine it should be written as 3x3 or 3^2. So the answer should be 2^3 x 3^2 because 9 can be divided into even more prime factors of 72.