# Question Video: Finding the Expression of a Function Transformation

Consider the function π(π₯) = π₯Β² β 3π₯ β 4. Find π(π₯ + 3).

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### Video Transcript

Consider the function π of π₯ equals π₯ squared minus three π₯ minus four. Find π of π₯ plus three.

In order to find π of π₯ plus three, we need to replace all of the π₯s with π₯ plus three. So essentially, weβre replacing π₯ with π₯ plus three and then evaluating. So here we can see weβve replaced π₯ with π₯ plus three.

And now we need to evaluate this. π₯ plus three squared is π₯ plus three times π₯ plus three. And then we also need to distribute the negative three to the π₯ plus three in the middle. π₯ times π₯ is π₯ squared. π₯ times three is three π₯. Three times π₯ is three π₯. And three times three is nine.

And now we will distribute negative three to π₯ plus three. Negative three times π₯ is negative three π₯. And negative three times three is negative nine. And then we bring down our minus four.

So now we need to combine like terms. Our highest power is two. So π₯ squared needs to go first. Now we can combine all of the π₯s. Three π₯ plus three π₯ minus three π₯ is three π₯. And now for the numbers, the constants, nine, negative nine, and negative four make negative four. Therefore, π of π₯ plus three is equal to π₯ squared plus three π₯ minus four.