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Select the correct answer.

Which of these is the standard form of the following function?

1. [tex]f(x) = -9(x+5)^2 + 4[/tex]
2. [tex]f(x) = 9x^2 - 90x - 221[/tex]
3. [tex]f(x) = -9x^2 - 180x - 221[/tex]
4. [tex]f(x) = 9x^2 - 180x + 221[/tex]
5. [tex]f(x) = -9x^2 - 90x - 221[/tex]

Answer :

To convert the function from vertex form to standard form, follow these steps:

1. Start with the given function in vertex form:
[tex]$$f(x) = -9(x+5)^2 + 4.$$[/tex]

2. Expand the square [tex]$(x+5)^2$[/tex]. Recall:
[tex]$$ (x+5)^2 = x^2 + 10x + 25.$$[/tex]

3. Multiply the expanded form by [tex]$-9$[/tex]:
[tex]$$-9(x^2 + 10x + 25) = -9x^2 - 90x - 225.$$[/tex]

4. Finally, add [tex]$4$[/tex] to the expression:
[tex]$$-9x^2 - 90x - 225 + 4 = -9x^2 - 90x - 221.$$[/tex]

Thus, the standard form of the function is:
[tex]$$f(x) = -9x^2 - 90x - 221.$$[/tex]

This corresponds to option 5.

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