Find out the symmetry of equations, Algebra

Assignment Help:

Find out the symmetry of equations.

                                                 y = x2 - 6x4 + 2

Solution

First we'll check for symmetry around the x-axis. It means that we have to replace all the y's with -y. That's simple enough to do in this case since there is only one y.

- y = x2 - 6x4 + 2

Now, it is not an equal equation as the terms onto the right are alike to the original equation & the term on the left is the opposite sign.  So, this equation doesn't have symmetry around the x-axis.

Next, let's verify symmetry around the y-axis.  we'll replace all x's with -x here.

                                  y = ( - x )2 - 6 ( - x )4  + 2

                                   y = x2 - 6x4 + 2

Later than simplifying we got precisely the similar equation back out that means that the two are equivalent. Thus, this equation does have symmetry around the y-axis.

At last, we have to check for symmetry around the origin.  Here we replace both variables.

- y = ( - x )2  - 6 ( - x )4  + 2

- y = x2 - 6x4 + 2

Thus, as with the first test, the left side is distinct from the original equation & the right side is the same to the original equation. Thus, it isn't equivalent to the original equation & we don't contain symmetry regarding the origin.


Related Discussions:- Find out the symmetry of equations

Prime factorization tree method, I am trying to figure out how the tree met...

I am trying to figure out how the tree method works for number 47

Angles and sides, what is the missing angle of 37 degree and 92 drgees

what is the missing angle of 37 degree and 92 drgees

Convert following into the function, Convert following into the form    ...

Convert following into the form                                        f (x ) = a ( x - h ) 2  + k Solution We are going to complete the square here.  Though, it is a s

Fact of augmented matrix, Fact Following any system of equations there ...

Fact Following any system of equations there are accurately three possibilities for the solution. 1.   There will not be a solution. 2.   There will be just one solution.

Word problems, omar loves bags of potato chips and ice cream bars, and they...

omar loves bags of potato chips and ice cream bars, and they have fat and calories as follows: bags of potato chips contain 12 grams of fat and 325 calories; ice cream bars contain

Standard form, 4(x)^2-40x+107 in standard form

4(x)^2-40x+107 in standard form

True inequality, We have to give one last note on interval notation before ...

We have to give one last note on interval notation before moving on to solving inequalities. Always recall that while we are writing down an interval notation for inequality that t

Ratio and propotion, 4 pipes can fill a tank in 70 minutes.how long will it...

4 pipes can fill a tank in 70 minutes.how long will it take to fill the tank by 7 pipes

Graphing functions, Now we need to discuss graphing functions. If we recall...

Now we need to discuss graphing functions. If we recall from the earlier section we said that f ( x ) is nothing more than a fancy way of writing y. It means that already we kno

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd