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Let suppose we have a simple U shaped vertical parabola whose vertex lies on $(0,0)$.
To move it $h$ units up, we subtract $2$ from $x$ and vice versa. Same for $k$ and $y$ axis.
This seems pretty natural now.

When I learned it for the first time, I thought - to go up we should add to $x$ (not subtract). The logic was never explained (or maybe I didn't recognize it). The teacher gave no reason (and even I didn't ask).

Today this question again popped up in my brain. So,
Why adding $h$ in $x$ in the equation, subtracts $h$ from the value of $x$ axis?

What is the logic behind this?

Dhruv Joshi
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Sujay Bhaskar
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1 Answers1

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By going up or down what we are doing is translating the axis, let say you want to go $h$ units up and $k$ units right, let our new coordinate system be $(X,Y)$, by our translation $(x,y)$ become $(X,Y)$, i.e $$(x+k,y+h) =(X,Y)$$

equating the respective coordinates we get $$X-k=x$$ $$Y-h=y$$

notice our new coordinates system is in ($X,Y$), but your equation was in ($x,y$) replace $x$ and $y$ in that equation with the above-obtained expression to get the equation in our new coordinate system, now you can rename $X$ and $Y$ as $x$ and $y$ respectively.

A quick and easy way to see this is to observe where the origin has shifted.

Dhruv Joshi
  • 100