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π of π₯ is equal to π₯ squared minus four π₯ plus two.
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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.
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Find the value of π.
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Well, the question told us that the function is translated π, so positive π, units in the π¦-direction.
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Well, that means β and itβs creating function π of π₯.
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So, that means π of π₯ is π of π₯ plus π.
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Now, we were told that π of π₯ is equal to π₯ squared minus four π₯ plus nine.
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So, we can replace that in our equation.
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And we were told that π of π₯ is equal to π₯ squared minus four π₯ plus two.
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So, we can replace that in our equation.
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And then, lastly, weβve just got to add the π to the end.
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So, now, we can rearrange and solve this equation.
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Subtracting π₯ squared from both sides gives me this.
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Then, adding four π₯ to both sides gives me this.
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And finally, subtracting two from both sides gives me this.
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π is equal to seven.
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And if Iβve got enough time, like at the end of an exam, I can check that answer.
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Translating a function by π units in the π¦-direction is like doing π of π₯ plus π.
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So, if we reckon the answer π is equal to seven, we can work out π of π₯ plus seven.
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So, we got π of π₯, our original π of π₯ function.
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And we just add seven to the π¦-coordinates like we do there.
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And that gives us π₯ squared minus four π₯ plus nine, which indeed is the same as π of π₯.
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So, we know weβve got the right answer.