Answer:
We conclude that the standard form of the given function is:
[tex]f(x)=-9x^2-90x-221[/tex]
Hence, option B is correct.
Step-by-step explanation:
We know that the standard form of the quadratic function is of the form
[tex]f\left(x\right)\:=\:ax^2\:+\:bx\:+\:c[/tex]
Given the function
[tex]f(x)=-9\left(x\:+\:5\right)^2\:+\:4[/tex]
as (x+5)² = x² + 10x + 25
[tex]f(x)=-9\left(x^2+10x+25\right)+4[/tex]
Expanding -9(x² + 10x + 25) = -9x² - 90x - 225
[tex]f\left(x\right)\:=-9x^2-90x-225+4[/tex]
simplifying
[tex]f(x)=-9x^2-90x-221[/tex]
Therefore, we conclude that the standard form of the given function is:
[tex]f(x)=-9x^2-90x-221[/tex]
Hence, option B is correct.
