Conceptual question on equations of the form ##x=ay^2+by+c##

[chwala]

Homework Statement

This is my own question;

Relevant Equations

quadratic equations

Now i just need some clarification; we know that quadratic equations are equations of the form $y=ax^2+bx+c$ with $a,b$ and $c$ being constants and $x$ and $y$ variables.

Now my question is... can we also view/look at $x=y^2+2y+1$ as quadratic equations having switched the variables ? thanks...

 

[SammyS]

Homework Statement: This is my own question;
Relevant Equations: quadratic equations

Now i just need some clarification; we know that quadratic equations are equations of the form $y=ax^2+bx+c$ with $a,b$ and $c$ being constants and $x$ and $y$ variables.

Now my question is... can we also view/look at $x=y^2+2y+1$ as quadratic equations having switched the variables ? thanks...

Yes. Of course we can.

However, I hope you realize that in this case, $x$ is a function of $y$, but $y$ is not a function of $x$.

 

[chwala]

Yes. Of course we can.

However, I hope you realize that in this case, $x$ is a function of $y$, but $y$ is not a function of $x$.

yes @SammyS ...we now have $x$ as the dependent variable......but is the relation going to be a Function? as we require to obtain one unique value( one and only one) for $y$ for any value of $xε\mathbb{R}$.

 

[nuuskur]

it is a function of variable $y$

 

[SammyS]

yes @SammyS ...we now have $x$ as the dependent variable......but is the relation going to be a Function? as we require to obtain one unique value( one and only one) for $y$ for any value of $xε\mathbb{R}$.

I believe that I answered this in Post #2 .

 

[MatinSAR]

as we require to obtain one unique value( one and only one) for $y$ for any value of $xε\mathbb{R}$.

But this is needed when $y$ is a function of $x$.
If we have $x=y^2$ we can say that $x$ is a function of $y$. But $y$ is not a function of $x$ because: $y=\pm x^\frac {1}{2}$.