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.
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.
