Transforming $y=f(x)$ to $y^2=f(x)$

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Given a graph $y=f(x)$, transformed to $y^2=f(x)$, how can I determine the gradient of the roots at $y=0$ and why? Take this graph as an example:
$y=f(x)$ transforms into $y^2=f(x)$



Particularly, the gradient at B and C are different. It was also said that gradient at B could be 0 instead.










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  • What are B and C?
    – Taroccoesbrocco
    Sep 5 at 5:17










  • The points at which the graph cuts the x-axis. Its shown in the picture link.
    – Ayuzus13
    Sep 5 at 5:32














up vote
0
down vote

favorite












Given a graph $y=f(x)$, transformed to $y^2=f(x)$, how can I determine the gradient of the roots at $y=0$ and why? Take this graph as an example:
$y=f(x)$ transforms into $y^2=f(x)$



Particularly, the gradient at B and C are different. It was also said that gradient at B could be 0 instead.










share|cite|improve this question





















  • What are B and C?
    – Taroccoesbrocco
    Sep 5 at 5:17










  • The points at which the graph cuts the x-axis. Its shown in the picture link.
    – Ayuzus13
    Sep 5 at 5:32












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Given a graph $y=f(x)$, transformed to $y^2=f(x)$, how can I determine the gradient of the roots at $y=0$ and why? Take this graph as an example:
$y=f(x)$ transforms into $y^2=f(x)$



Particularly, the gradient at B and C are different. It was also said that gradient at B could be 0 instead.










share|cite|improve this question













Given a graph $y=f(x)$, transformed to $y^2=f(x)$, how can I determine the gradient of the roots at $y=0$ and why? Take this graph as an example:
$y=f(x)$ transforms into $y^2=f(x)$



Particularly, the gradient at B and C are different. It was also said that gradient at B could be 0 instead.







graphing-functions transformation






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asked Sep 5 at 4:58









Ayuzus13

1




1











  • What are B and C?
    – Taroccoesbrocco
    Sep 5 at 5:17










  • The points at which the graph cuts the x-axis. Its shown in the picture link.
    – Ayuzus13
    Sep 5 at 5:32
















  • What are B and C?
    – Taroccoesbrocco
    Sep 5 at 5:17










  • The points at which the graph cuts the x-axis. Its shown in the picture link.
    – Ayuzus13
    Sep 5 at 5:32















What are B and C?
– Taroccoesbrocco
Sep 5 at 5:17




What are B and C?
– Taroccoesbrocco
Sep 5 at 5:17












The points at which the graph cuts the x-axis. Its shown in the picture link.
– Ayuzus13
Sep 5 at 5:32




The points at which the graph cuts the x-axis. Its shown in the picture link.
– Ayuzus13
Sep 5 at 5:32















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