# Video: Finding the Number of Units That a Function Is Translated in the π¦-Direction to Another One

π(π₯) = π₯Β²β 4π₯ + 2. The function is translated π units in the π¦-direction to create function π(π₯) = π₯Β² β 4π₯ + 9. Find the value of π.

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### Video Transcript

π of π₯ is equal to π₯ squared minus four π₯ plus two. The function is translated π units in the π¦-direction to create function π of π₯ is equal to π₯ squared minus four π₯ plus nine. Find the value of π.

Well, the question told us that the function is translated π, so positive π, units in the π¦-direction. Well, that means β and itβs creating function π of π₯. So, that means π of π₯ is π of π₯ plus π. Now, we were told that π of π₯ is equal to π₯ squared minus four π₯ plus nine. So, we can replace that in our equation. And we were told that π of π₯ is equal to π₯ squared minus four π₯ plus two. So, we can replace that in our equation. And then, lastly, weβve just got to add the π to the end. So, now, we can rearrange and solve this equation.

Subtracting π₯ squared from both sides gives me this. Then, adding four π₯ to both sides gives me this. And finally, subtracting two from both sides gives me this. π is equal to seven. And if Iβve got enough time, like at the end of an exam, I can check that answer. Translating a function by π units in the π¦-direction is like doing π of π₯ plus π. So, if we reckon the answer π is equal to seven, we can work out π of π₯ plus seven. So, we got π of π₯, our original π of π₯ function. And we just add seven to the π¦-coordinates like we do there. And that gives us π₯ squared minus four π₯ plus nine, which indeed is the same as π of π₯. So, we know weβve got the right answer.