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The graph of the function f(x) = x^2 is translated (shifted) up 3 units and left 4 units. Write an equation to represent the new function after the translations.

I know how to solve it but need help making an equation but I can solve it myself.

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facundo3141592

the translated function is:

g(x) = (x + 4)^2 + 3

How to find the equation of the translated function?

For a given function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

  • If N is positive, the translation is upwards.
  • If N is negative, the translation is downwards.

And a horizontal translation is written as:

g(x) = f(x + N)

  • If N is positive, the translation is to the left.
  • If N is negative, the translation is to the right.

So if we have a shift (translation) up of 3 units and left of 4 units, we have:

g(x) = f(x + 4) + 3

Here f(x) = x^2, then the translated function is:

g(x) = (x + 4)^2 + 3

If you want to learn more about translations, you can read:

https://brainly.com/question/24850937

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