Question

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

f(x) = -9(x + 5)2 + 4


f(x) = 9x2 − 90x − 221

f(x) = -9x2 − 90x − 221

f(x) = 9x2 − 180x + 221

f(x) = -9x2 − 180x − 221

Answer 1

Hope this helps!

Explanation:

Answer 2

We conclude that the standard form of the given function is:

`f(x)=-9x^2-90x-221`

Hence, option B is correct.

Explanation:

We know that the standard form of the quadratic function is of the form

`f\left(x\right)\:=\:ax^2\:+\:bx\:+\:c`

Given the function

`f(x)=-9\left(x\:+\:5\right)^2\:+\:4`

as (x+5)² = x² + 10x + 25

`f(x)=-9\left(x^2+10x+25\right)+4`

Expanding -9(x² + 10x + 25) = -9x² - 90x - 225

`f\left(x\right)\:=-9x^2-90x-225+4`

simplifying

`f(x)=-9x^2-90x-221`

Therefore, we conclude that the standard form of the given function is:

`f(x)=-9x^2-90x-221`

Hence, option B is correct.