Point (p, 4p²) on Curve y = 4x² for All p

[MASH4077]

Show that the point $$(p, 4p^{2})$$ lies on the curve $$y = 4x^{2}$$ for all real values of p.

I'm not at all sure how to go about answering this. I know that substituting p into $$y = 4x^{2}$$ satisfies the equation. Is that enough?, or I'm not looking at this deep enough. Any hint(s) appreciated.

Thanks.

 

[statdad]

Saying a point is on the graph given by some equation, you are saying the x- and y-coordinates satisfy that equation. So yes, since substituting x = p into your equation gives y = 4p^2, you know that $(p, 4p^2)$ is on the graph.

 

[MASH4077]

Looks like the question wasn't as difficult as I thought it was going to be.

Okay statdad thanks. :)

P.S. Appologies to moderators. I'll post these sorts of questions in the correct section next time. ;)